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Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework

T0 review · 2 major / 2 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read DMK fast summation extends to rectangular cuboids with mixed periodicity by cubical tiling of localized tree levels and Fourier treatment of the root contribution.

desk verdict DMK now works on rectangular cuboids with any mix of periodic and free directions by tiling for local tree parts and using truncated Fourier kernels at the root. read the letter →

arxiv 2606.27134 v1 pith:OFS54GFS submitted 2026-06-25 math.NA cs.NA

David Krantz , Ludvig af Klinteberg , Anna-Karin Tornberg This is my paper · ORCID
classification math.NAcs.NA
keywords fastsummationDMKmixedperiodicityrectangularcuboidsStokespotentialsEwaldmultilevelkernelsplittingoctree
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper extends the Dual-space multilevel kernel-splitting framework from free-space and fully periodic cubes to rectangular cuboids that may be periodic in one, two, or three directions. Lower levels of the octree involve only localized interactions, so they can be evaluated on a cubical tiling of the domain with almost no change to the original algorithm. The smooth root-level far-field term is computed in Fourier space, using series in periodic directions and integrals in free directions, with truncated kernels to regularize singularities when periodicity is reduced. The resulting scheme is validated on electrostatic and Stokes potentials for all periodicity combinations and a wide range of aspect ratios, and the added cost of periodization remains small even for high-aspect-ratio boxes.

What carries the argument

The periodization strategy that tiles localized lower-tree interactions on cubical domains and evaluates the root-level smooth contribution via Fourier series or integrals, regularized by truncated kernels when periodicity is incomplete.

What would settle it

A numerical run on a high-aspect-ratio cuboid with one periodic direction that shows the periodization overhead exceeding a small fraction of free-space DMK time, or that the truncated-kernel Fourier discretization fails to converge at the expected rate.

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Extended reading notes

Core claim

By evaluating localized interactions below the root on a cubical tiling and handling the smooth root-level far-field in Fourier space with truncated kernels for regularization, DMK applies to mixed-periodicity problems on rectangular cuboids while preserving the efficiency of the free-space version.

Load-bearing premise

Interactions on all tree levels below the root are localized, allowing their evaluation with minimal modification on a cubical tiling of the domain.

Editorial extensions

If this is right

  • The method applies to electrostatic potential as well as Stokeslet, stresslet and rotlet kernels for any combination of periodicities.
  • For large-aspect-ratio cuboids the root-level sum can be accelerated by the fast Fourier transform.
  • The approach supplies a general framework for other non-oscillatory kernels whenever a kernel split exists.
  • Numerical cost remains comparable to the free-space DMK algorithm across the tested range of aspect ratios.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same tiling-plus-Fourier-root strategy could be tested on other multilevel summation schemes that already separate local and smooth contributions.
  • Channel or slab geometries common in confined-flow simulations become directly accessible without forcing artificial periodicity in all directions.
  • The regularization via truncated kernels may generalize to kernels whose Fourier transforms have different singularity structures.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper extends the dual-space multilevel kernel-splitting (DMK) framework, originally for free-space and fully periodic cubic domains, to rectangular cuboids with periodicity in one, two, or three directions. It exploits localization of sub-root tree interactions to evaluate them on a cubical tiling with minimal changes, while treating the smooth root-level far-field via Fourier series (periodic directions) and integrals (free directions), regularized by truncated kernels for reduced periodicity to enable convergent trapezoidal rules. The approach is claimed to apply to non-oscillatory kernels admitting a split (e.g., electrostatic potential, Stokeslet/stresslet/rotlet) and to incur only small overhead relative to free-space DMK, even at high aspect ratios; validation is asserted via numerical experiments across all periodicities and aspect ratios.

Significance. If the error analysis, convergence rates, and numerical results hold, the work supplies a practical, unified fast-summation tool for mixed-periodicity problems on cuboids that preserves DMK's multilevel structure and extends naturally to other kernels. The combination of established FMM/Ewald/multilevel ideas with a new handling of truncated Fourier kernels for arbitrary periodicity is a clear incremental advance in the field of fast summation methods.

major comments (2)
  1. [§3] §3 (periodization strategy) and the abstract claim that sub-root interactions are 'localized' and therefore evaluable on a cubical tiling with 'minimal modification'; however, the precise definition of the interaction cutoff radius relative to the cuboid aspect ratio and the resulting error bound when the tiling is non-cubic are not stated explicitly, which is load-bearing for the 'small overhead' claim across high-aspect-ratio cases.
  2. [§4] The abstract and §4 assert that truncated kernels yield 'rapidly convergent trapezoidal discretizations' for all periodicities, but no explicit truncation-error estimate or dependence on the truncation parameter appears; without this, it is unclear whether the unified treatment maintains the same convergence order as the fully periodic case.
minor comments (2)
  1. [§4] Notation for the truncated kernel (e.g., K_trunc) should be introduced once and used consistently; several paragraphs in §4 switch between K^trunc and K_tr without definition.
  2. [Numerical results] Figure captions for the numerical experiments should include the specific aspect ratios tested and the number of particles per run so that the 'wide range' claim can be assessed without consulting the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. We address the two major comments point by point below. Both points identify places where explicit statements are missing from the current manuscript; we will add the requested definitions and estimates in the revision.

read point-by-point responses

  1. Referee: [§3] §3 (periodization strategy) and the abstract claim that sub-root interactions are 'localized' and therefore evaluable on a cubical tiling with 'minimal modification'; however, the precise definition of the interaction cutoff radius relative to the cuboid aspect ratio and the resulting error bound when the tiling is non-cubic are not stated explicitly, which is load-bearing for the 'small overhead' claim across high-aspect-ratio cases.

    Authors: We agree that the cutoff radius and the associated tiling error bound should be stated explicitly. The cutoff at every sub-root level is set by the finite support of the localized kernel component after the split; this support depends only on the octree level and the splitting parameter, remaining independent of the cuboid aspect ratio. Consequently the number of tiled neighbor interactions per source particle stays O(1) regardless of aspect ratio. We will insert a short paragraph in §3 that (i) defines the cutoff radius in terms of the octree depth and kernel support length and (ii) bounds the tiling error by the tail of the smooth kernel, which decays exponentially. This addition directly supports the small-overhead claim. revision: yes

  2. Referee: [§4] The abstract and §4 assert that truncated kernels yield 'rapidly convergent trapezoidal discretizations' for all periodicities, but no explicit truncation-error estimate or dependence on the truncation parameter appears; without this, it is unclear whether the unified treatment maintains the same convergence order as the fully periodic case.

    Authors: We acknowledge that an explicit truncation-error estimate is absent and would strengthen the justification for uniform convergence order. While the numerical experiments already illustrate rapid convergence for all periodicities, we will add a brief analytic paragraph in §4 deriving that the truncation error of the regularized Fourier kernels decays exponentially with the truncation radius. This error is independent of the trapezoidal discretization and therefore does not degrade the spectral accuracy already established for the fully periodic case. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in the derivation chain

full rationale

The paper extends the existing DMK framework (free-space and fully periodic cube cases) by exploiting the localization of sub-root tree interactions to enable cubical tiling for periodization, then applies standard Fourier series/integrals with truncated kernels at the root level for arbitrary periodicity. No equation or claim reduces by construction to a fitted parameter, self-definition, or unverified self-citation chain; the central construction combines established FMM-style trees, Ewald-style Fourier treatment, and multilevel splitting without internal reduction to its own inputs. Numerical experiments serve as validation rather than definitional necessity. The derivation is self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

Ledger constructed from abstract only; no explicit fitted parameters or new entities are named.

assumptions (2)
  • domain assumption Interactions on tree levels below the root remain localized enough to be evaluated on a cubical tiling of the rectangular domain with minimal modification.
    Stated as the enabling fact for the periodization of all levels except the root.
  • domain assumption Truncated kernels regularize singular and near-singular Fourier kernels sufficiently to produce rapidly convergent trapezoidal discretizations.
    Invoked for the reduced-periodicity cases to unify the Fourier treatment.

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Cite this review

Pith. "Pith review of Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework." pith.science (2026). https://pith.science/paper/OFS54GFS

@misc{pith2026260627134,
  author       = {Pith},
  title        = {Pith review of: Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OFS54GFS}},
  note         = {Machine review of arXiv:2606.27134}
}
read the original abstract

Dual-space multilevel kernel-splitting (DMK) is a fast summation framework that combines ideas from the fast multipole method, Ewald summation, and multilevel summation. Originally formulated for free-space problems, and later extended to fully periodic problems on a cube, it decomposes the kernel interaction into a smooth global contribution and a hierarchy of localized interactions evaluated on an octree. We extend DMK to problems on rectangular cuboids with periodic boundary conditions in one, two, or three coordinate directions. The periodization leverages the fact that interactions on all tree levels below the root are localized, allowing for their evaluation with minimal modification on a cubical tiling of the domain. The remaining smooth root-level far-field contribution is evaluated in Fourier space, with Fourier series in the periodic directions and Fourier integrals in the free directions. For reduced periodicity, truncated kernels are used to regularize singular and near-singular Fourier kernels, yielding rapidly convergent trapezoidal discretizations and a unified treatment of all periodicities. For large-aspect-ratio cuboids, the root-level sum can be accelerated using the fast Fourier transform. We validate the method for the electrostatic potential and Stokeslet, stresslet and rotlet potentials, for all periodicities and a wide range of aspect ratios. Numerical experiments show that the periodization adds only a small overhead to the original free-space DMK algorithm, also for high-aspect-ratio cuboids. The resulting method provides a framework for applying DMK to problems with mixed periodicity on rectangular cuboids, and extends naturally to other non-oscillatory kernels for which a kernel split is available.

Figures

Figures reproduced from arXiv: 2606.27134 by the authors.

Figure 3
Figure 3. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 3.1
Figure 3.1. A 2D sketch of how the truncation radius [PITH_FULL_IMAGE:figures/full_fig_p008_3_1.png] view at source ↗
Figure 3
Figure 3. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: a [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 4.1
Figure 4.1. Figure 4.1: Cube tiling for a triply periodic cuboid. Panel (a) shows and exact tiling, while panel (b) shows [PITH_FULL_IMAGE:figures/full_fig_p010_4_1.png]
Figure 4.2
Figure 4.2. Figure 4.2: A sketch of the domain Ωext (outer red line) in the 1−2 plane for evaluation of u DP compact, as defined in (2.3) with D = 2 or 3 and L2 not an integer multiple of L1. Sources inside Ω in black, periodic copies of these sources in blue. Each of the red Mext cubes wil…
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 4.3
Figure 4.3. Figure 4.3: Depending on the domain, the structure factor [PITH_FULL_IMAGE:figures/full_fig_p012_4_3.png]
Figure 6.1
Figure 6.1. Figure 6.1: Panels (a), (b), and (c) show the total number of Fourier discretization points [PITH_FULL_IMAGE:figures/full_fig_p022_6_1.png]
Figure 6
Figure 6. Figure 6: a [PITH_FULL_IMAGE:figures/full_fig_p022_6.png]
Figure 6.2
Figure 6.2. Figure 6.2: Linear scaling of periodic DMK for the Laplace kernel on the unit cube. The figure shows the runtime [PITH_FULL_IMAGE:figures/full_fig_p023_6_2.png]
Figure 6
Figure 6. Figure 6: a [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]
Figure 6.3
Figure 6.3. Figure 6.3: Normalized runtime for rectangular cells [PITH_FULL_IMAGE:figures/full_fig_p024_6_3.png]
Figure 6.4
Figure 6.4. Figure 6.4: Runtimes and self-normalized runtimes of the compact and far-field contributions, [PITH_FULL_IMAGE:figures/full_fig_p025_6_4.png]
Figure 6.5
Figure 6.5. Figure 6.5: Large-aspect-ratio version of [PITH_FULL_IMAGE:figures/full_fig_p025_6_5.png]
Figure 6.6
Figure 6.6. Figure 6.6: Panel (a) illustrates the singly periodic pipe geometry in the cell [PITH_FULL_IMAGE:figures/full_fig_p025_6_6.png]

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

288 extracted references · 198 canonical work pages · cited by 1 Pith paper

  1. [1]

    A Method to Compute Periodic Sums , author =. J. Comput. Phys. , volume = 272, pages =. doi:10.1016/j.jcp.2014.04.039 , urldate =

    work page doi:10.1016/j.jcp.2014.04.039 2014

  2. [2]

    and Marple, Gary R

    Barnett, Alex H. and Marple, Gary R. and Veerapaneni, Shravan and Zhao, Lin , year = 2018, month = nov, journal =. A. doi:10.1002/cpa.21759 , urldate =

    work page doi:10.1002/cpa.21759 2018

  3. [3]

    Pressure Tensor for Electrostatic Interaction Calculated by Fast Multipole Method with Periodic Boundary Condition , author =. J. Comput. Chem. , volume =. doi:10.1002/jcc.25179 , urldate =

    work page doi:10.1002/jcc.25179

  4. [5]

    A scalable Ewald-free BIE framework for periodic Stokes flow via hierarchical proxy sums

    Tianyue Li and Dhairya Malhotra and Shravan Veerapaneni , year=. 2605.30805 , archivePrefix=

    work page Pith review arXiv

  5. [6]

    (2000), Calculation of atomic integration data

    Amisaki, Takashi , year = 2000, month = sep, journal =. Precise and Efficient. doi:10.1002/1096-987X(200009)21:12<1075::AID-JCC4>3.0.CO;2-L , langid =

    work page doi:10.1002/1096-987x(200009)21:12 2000

  6. [7]

    Liang, L

    Liang, Jiuyang and Lu, Libin and Barnett, Alex and Greengard, Leslie and Jiang, Shidong , year = 2026, month = may, journal =. Accelerating Molecular Dynamics Simulations Using Fast. doi:10.1038/s41467-026-73232-8 , urldate =

    work page doi:10.1038/s41467-026-73232-8 2026

  7. [8]

    Efficient numerical methods for non-local operators:

    B. Efficient numerical methods for non-local operators:. 2010 , publisher=

    2010

  8. [9]

    Hackbusch, Wolfgang and B. Appl. Numer. Math. , volume=. 2002 , publisher=

    2002

Show all 288 references
  1. [10]

    Computing , volume =

    Giebermann, Klaus , year =. Computing , volume =. doi:10.1007/s006070170005 , isbn =

    doi

  2. [11]

    , year =

    Wang, Mu and Brady, John F. , year =. Spectral. J. Comput. Phys. , volume =

  3. [12]

    Parameter

    Nestler, Franziska , year =. Parameter. Front. Phys. , volume =

  4. [13]

    Wu, Bowei and Zhu, Hai and Barnett, Alex and Veerapaneni, Shravan , journal =

  5. [14]

    and Tornberg, Anna Karin , doi =

    Broms, Anna and Barnett, Alex H. and Tornberg, Anna Karin , doi =. J. Comput. Phys. , keywords =

  6. [15]

    Accelerating Fast

    Jiuyang Liang and Libin Lu and Alex Barnett and Leslie Greengard and Shidong Jiang , journal=. Accelerating Fast. 2025 , volume=

    2025

  7. [16]

    Fast Summation of. J. Comput. Phys. , volume =

  8. [17]

    2602.16591 , archivePrefix=

    Erik Boström and Anna-Karin Tornberg and Ludvig af Klinteberg , year=. 2602.16591 , archivePrefix=

    arXiv

  9. [18]

    A. SIAM J. Sci. Comput. , author =. 2019 , pages =

    2019

  10. [19]

    Bottom-up construction and 2:1 balance refinement of linear octrees in parallel , author=. SIAM J. Sci. Comput. , volume=. 2008 , publisher=

    2008

  11. [20]

    A new version of the adaptive fast

    Greengard, Leslie and Jiang, Shidong and Rachh, Manas and Wang, Jun , journal=. A new version of the adaptive fast. 2024 , publisher=

    2024

  12. [21]

    1972 , publisher=

    Fourier Series and Integrals , author=. 1972 , publisher=

    1972

  13. [22]

    Ethridge and L

    F. Ethridge and L. Greengard , title =. SIAM J. Sci. Comput. , year =

  14. [23]

    Dutt and V

    A. Dutt and V. Rokhlin , TITLE =. SIAM J. Sci. Comput. , VOLUME =. 1993 , PAGES =

    1993

  15. [24]

    Dutt and V

    A. Dutt and V. Rokhlin , TITLE =. Appl. Comput. Harmon. Anal. , VOLUME =. 1995 , PAGES =

    1995

  16. [25]

    and Nieslony, A

    Potts, Daniel and Steidl, G. and Nieslony, A. , title =. Numer. Math. , volume =. 2004 , pages =

    2004

  17. [26]

    Multilevel matrix multiplication and fast solution of integral equations , author=. J. Comput. Phys. , volume=. 1990 , publisher=

    1990

  18. [27]

    and Venner, C

    Brandt, A. and Venner, C. H. , title =. SIAM J. Sci. Comput. , volume =. 1998 , doi =

    1998

  19. [28]

    and Wu, Zhe and Phillips, James C

    Hardy, David J. and Wu, Zhe and Phillips, James C. and Stone, John E. and Skeel, Robert D. and Schulten, Klaus , title =. J. Chem. Theory Comput. , volume =. 2015 , doi =

    2015

  20. [29]

    and Zhang, Hao and Komatsu, Teruhisa S

    Morimoto, Gentaro and Koyama, Yohei M. and Zhang, Hao and Komatsu, Teruhisa S. and Ohno, Yousuke and Nishida, Keigo and Ohmura, Itta and Koyama, Hiroshi and Taiji, Makoto , year =. Hardware Acceleration of Tensor-Structured Multilevel Ewald Summation Method on. Proc. doi:10.11...

    doi

  21. [30]

    A fast adaptive multipole algorithm in three dimensions , author=. J. Comput. Phys. , volume=. 1999 , publisher=

    1999

  22. [31]

    Malhotra , Title =

    D. Malhotra , Title =. 2022 , Howpublished =

    2022

  23. [32]

    Askham and Z

    T. Askham and Z. Gimbutas and L. Greengard and L. Lu and M. O'Neil and M. Rachh and V. Rokhlin , Title =. 2021 , Howpublished =

    2021

  24. [33]

    Gimbtuas and L

    Z. Gimbtuas and L. Greengard and L. Lu and J. Magland and D. Malhotra and M. O'Neil and M. Rachh and V. Rokhlin , title =

  25. [34]

    Malhotra , title =

    D. Malhotra , title =

  26. [35]

    Second kind integral equations for the first kind

    Jiang, Shidong and Ren, Bo and Tsuji, Paul and Ying, Lexing , journal=. Second kind integral equations for the first kind. 2011 , publisher=

    2011

  27. [36]

    1988 , publisher=

    The rapid evaluation of potential fields in particle systems , author=. 1988 , publisher=

    1988

  28. [37]

    Prolate spheroidal wave functions,

    Landau, Henry J and Pollak, Henry O , journal=. Prolate spheroidal wave functions,. 1961 , publisher=

    1961

  29. [38]

    Prolate spheroidal wave functions,

    Slepian, David and Pollak, Henry O , journal=. Prolate spheroidal wave functions,. 1961 , publisher=

    1961

  30. [39]

    Prolate spheroidal wave functions,

    Slepian, David , journal=. Prolate spheroidal wave functions,. 1978 , publisher=

    1978

  31. [40]

    Some comments on

    Slepian, David , journal=. Some comments on. 1983 , publisher=

    1983

  32. [41]

    The Journal of Physical Chemistry A , author =

    An. The Journal of Physical Chemistry A , author =. 2020 , pages =. doi:10.1021/acs.jpca.0c01684 , abstract =

    2020 doi

  33. [42]

    A dual-space multilevel kernel-splitting framework for discrete and continuous convolution , author=. Comm. Pure Appl. Math. , volume=. 2025 , publisher=

    2025

  34. [43]

    doi:10.48550/arXiv.2408.10205 , abstract =

    Liu, Ziming and Ma, Pingchuan and Wang, Yixuan and Matusik, Wojciech and Tegmark, Max , month = aug, year =. doi:10.48550/arXiv.2408.10205 , abstract =

    doi

  35. [44]

    and Tegmark, Max , month = jun, year =

    Liu, Ziming and Wang, Yixuan and Vaidya, Sachin and Ruehle, Fabian and Halverson, James and Soljačić, Marin and Hou, Thomas Y. and Tegmark, Max , month = jun, year =. doi:10.48550/arXiv.2404.19756 , abstract =

    doi arXiv

  36. [45]

    SIAM Review , author =

    Exactness of. SIAM Review , author =. 2022 , pages =. doi:10.1137/20M1389522 , abstract =

    2022 doi

  37. [46]

    Fast. J. Comput. Phys. , author =. 2023 , pages =. doi:10.1016/j.jcp.2023.112473 , language =

    2023 doi

  38. [47]

    Optimal approximation using complex-valued neural networks , url =

    Geuchen, Paul and Voigtlaender, Felix , month = oct, year =. Optimal approximation using complex-valued neural networks , url =. doi:10.48550/arXiv.2303.16813 , abstract =

    doi

  39. [48]

    epubs.siam.org redirect -

  40. [49]

    Helsing, Johan and Jiang, Shidong , month = nov, year =. The

  41. [50]

    Recursive reduction quadrature for the evaluation of

    Jiang, Shidong and Zhu, Hai , month = nov, year =. Recursive reduction quadrature for the evaluation of

  42. [51]

    and Chuang, Isaac L

    Nielsen, Michael A. and Chuang, Isaac L. , year =. Quantum computation and quantum information , isbn =

  43. [52]

    Acta Numerica , author =

    Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation , volume =. Acta Numerica , author =. 2021 , pages =. doi:10.1017/S0962492921000039 , abstract =

    2021 doi

  44. [53]

    Loss landscapes and optimization in over-parameterized non-linear systems and neural networks , volume =. Appl. Comput. Harmon. Anal. , author =. 2022 , pages =. doi:10.1016/j.acha.2021.12.009 , language =

    2022 doi

  45. [54]

    Nature Machine Intelligence , author =

    Closed-form continuous-time neural networks , volume =. Nature Machine Intelligence , author =. 2022 , pages =. doi:10.1038/s42256-022-00556-7 , abstract =

    2022 doi

  46. [55]

    Hammad, M. M. , month = jul, year =. Comprehensive. doi:10.48550/arXiv.2407.19258 , abstract =

    doi

  47. [56]

    IEEE/CAA Journal of Automatica Sinica , author =

    Complex-. IEEE/CAA Journal of Automatica Sinica , author =. 2022 , pages =. doi:10.1109/JAS.2022.105743 , abstract =

    2022 doi

  48. [57]

    IEEE Transactions on Neural Networks and Learning Systems , author =

    Design of. IEEE Transactions on Neural Networks and Learning Systems , author =. 2024 , pages =. doi:10.1109/TNNLS.2022.3224779 , abstract =

    2024 doi

  49. [58]

    , month = feb, year =

    Trabelsi, Chiheb and Bilaniuk, Olexa and Zhang, Ying and Serdyuk, Dmitriy and Subramanian, Sandeep and Santos, João Felipe and Mehri, Soroush and Rostamzadeh, Negar and Bengio, Yoshua and Pal, Christopher J. , month = feb, year =. Deep

  50. [59]

    High-order discretization of a stable time-domain integral equation for. J. Comput. Phys. , author =. 2020 , keywords =. doi:10.1016/j.jcp.2019.109047 , language =

    2020 doi

  51. [60]

    SIAM Journal on Numerical Analysis , author =

    On the. SIAM Journal on Numerical Analysis , author =. 2022 , pages =. doi:10.1137/21M1456935 , abstract =

    2022 doi

  52. [62]

    Fast, high-order numerical evaluation of volume potentials via polynomial density interpolation , volume =. J. Comput. Phys. , author =. 2024 , pages =. doi:10.1016/j.jcp.2024.113091 , language =

    2024 doi

  53. [63]

    On quadrature for singular integral operators with complex symmetric quadratic forms , url =

    Hoskins, Jeremy and Rachh, Manas and Wu, Bowei , month = dec, year =. On quadrature for singular integral operators with complex symmetric quadratic forms , url =

  54. [64]

    SIAM Journal on Numerical Analysis , author =

    A. SIAM Journal on Numerical Analysis , author =. 2023 , pages =. doi:10.1137/22M1520372 , abstract =

    2023 doi

  55. [66]

    Fast multipole methods for evaluation of layer potentials with locally-corrected quadratures , url =

    Greengard, Leslie and O'Neil, Michael and Rachh, Manas and Vico, Felipe , month = apr, year =. Fast multipole methods for evaluation of layer potentials with locally-corrected quadratures , url =. doi:10.1016/j.jcpx.2021.100092 , abstract =

    2021 doi

  56. [67]

    Computers & Mathematics with Applications , author =

    An efficient full-wave solver for eddy currents , volume =. Computers & Mathematics with Applications , author =. 2022 , pages =. doi:10.1016/j.camwa.2022.10.018 , language =

    2022 doi

  57. [68]

    Comparison of integral equations for the. Adv. Comput. Math. , author =. 2021 , pages =. doi:10.1007/s10444-021-09904-4 , abstract =

    2021 doi

  58. [69]

    Integral Equations and Operator Theory , author =

    Dirac. Integral Equations and Operator Theory , author =. 2021 , pages =. doi:10.1007/s00020-021-02657-1 , abstract =

    2021 doi

  59. [70]

    SIAM Journal on Numerical Analysis , author =

    Cut. SIAM Journal on Numerical Analysis , author =. 2024 , pages =. doi:10.1137/22M1542933 , abstract =

    2024 doi

  60. [71]

    A. SIAM J. Sci. Comput. , author =. 2019 , keywords =. doi:10.1137/18M120885X , number =

    2019 doi

  61. [72]

    A. H. Barnett and others , title =. 2018 , Howpublished =

    2018

  62. [73]

    Blackwell and L

    R. Blackwell and L. Greengard and S. Jiang and D. Malhotra , title =. 2025 , Howpublished =

    2025

  63. [74]

    af Klinteberg , title =

    L. af Klinteberg , title =. 2025 , Howpublished =

    2025

  64. [75]

    Fast and accurate integral equation methods with applications in microfluidics , url =

    af Klinteberg, Ludvig , year =. Fast and accurate integral equation methods with applications in microfluidics , url =

  65. [76]

    Physical Review E , author =

    Generalized approach to. Physical Review E , author =. 2007 , pages =. doi:10.1103/PhysRevE.75.056706 , language =

    2007 doi

  66. [77]

    Mathematics of Computation , author =

    Numerical solution of the. Mathematics of Computation , author =. 1968 , pages =. doi:10.1090/S0025-5718-1968-0242392-2 , abstract =

    1968 doi

  67. [78]

    Acta Mechanica , author =

    Particle-scale computational approaches to model dry and saturated granular flows of non-. Acta Mechanica , author =. 2019 , pages =. doi:10.1007/s00707-019-02389-9 , abstract =

    2019 doi

  68. [79]

    A boundary integral equation approach to computing eigenvalues of the. Adv. Comput. Math. , author =. 2020 , pages =. doi:10.1007/s10444-020-09774-2 , abstract =

    2020 doi

  69. [80]

    Commun. Comput. Phys. , author =. 2015 , pages =. doi:10.4208/cicp.020215.150515sw , abstract =

    2015 doi

  70. [81]

    International Journal of Multiphase Flow , author =

    On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows , volume =. International Journal of Multiphase Flow , author =. 2012 , pages =. doi:10.1016/j.ijmultiphaseflow.2011.12.002 , abstract =

    2012 doi

  71. [83]

    A highly accurate boundary integral equation method for surfactant-laden drops in. J. Comput. Phys. , author =. 2018 , pages =. doi:10.1016/j.jcp.2018.01.033 , language =

    2018 doi

  72. [84]

    Molecular Physics , author =

    Yukawa potentials in systems with partial periodic boundary conditions. Molecular Physics , author =. 2007 , pages =. doi:10.1080/00268970701481716 , language =

    2007 doi

  73. [85]

    Molecular Physics , author =

    Ewald method for simulating. Molecular Physics , author =. 1996 , pages =. doi:10.1080/00268979609484516 , language =

    1996 doi

  74. [86]

    Neuroradiology , author =

    Evaluation of x-ray. Neuroradiology , author =. 1978 , pmid =. doi:10.1007/BF00395366 , abstract =

    1978 doi

  75. [87]

    ACM Computing Surveys , author =

    An introduction to quantum computing for non-physicists , volume =. ACM Computing Surveys , author =. 2000 , pages =. doi:10.1145/367701.367709 , abstract =

    2000 doi

  76. [88]

    Results in Physics , author =

    The extended. Results in Physics , author =. 2023 , keywords =. doi:10.1016/j.rinp.2023.106755 , abstract =

    2023 doi

  77. [89]

    npj Quantum Information , author =

    Quantum algorithms: an overview , volume =. npj Quantum Information , author =. 2016 , pages =. doi:10.1038/npjqi.2015.23 , abstract =

    2016 doi

  78. [90]

    2015 , pages =

    International Journal for Numerical Methods in Engineering , author =. 2015 , pages =. doi:10.1002/nme.4823 , abstract =

    2015 doi

  79. [91]

    Reviews in Chemical Engineering , author =

    Immersed boundary method for multiphase transport phenomena , volume =. Reviews in Chemical Engineering , author =. 2022 , pages =. doi:10.1515/revce-2019-0076 , abstract =

    2022 doi

  80. [92]

    arXiv:2308.00292 [math.NA] , author =

    A. arXiv:2308.00292 [math.NA] , author =. 2023 , note =

    2023

  81. [93]

    A cut finite element method for incompressible two-phase. J. Comput. Phys. , author =. 2019 , pages =. doi:10.1016/j.jcp.2019.01.028 , language =

    2019 doi

  82. [94]

    SIAM Journal on Numerical Analysis , author =

    Robust and. SIAM Journal on Numerical Analysis , author =. 2015 , pages =. doi:10.1137/140973992 , abstract =

    2015 doi

  83. [95]

    A scalable computational platform for particulate. J. Comput. Phys. , author =. 2020 , pages =. doi:10.1016/j.jcp.2020.109524 , language =

    2020 doi

  84. [96]

    On the numerical evaluation of the prolate spheroidal wave functions of order zero , volume =. Appl. Comput. Harmon. Anal. , author =. 2022 , pages =. doi:10.1016/j.acha.2022.02.002 , language =

    2022 doi

  85. [97]

    An. SIAM J. Sci. Comput. , author =. 2023 , pages =. doi:10.1137/22M153495X , abstract =

    2023 doi

  86. [98]

    Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology , volume =. Adv. Comput. Math. , author =. 2023 , pages =. doi:10.1007/s10444-023-10083-7 , abstract =

    2023 doi

  87. [99]

    Efficient convergent boundary integral methods for slender bodies , volume =. J. Comput. Phys. , author =. 2024 , pages =. doi:10.1016/j.jcp.2024.112855 , language =

    2024 doi

  88. [100]

    IEEE Journal on Multiscale and Multiphysics Computational Techniques , author =

    Design of perfectly conducting objects that are invisible to an incident plane wave , issn =. IEEE Journal on Multiscale and Multiphysics Computational Techniques , author =. 2024 , pages =. doi:10.1109/JMMCT.2024.3364084 , abstract =

    2024 doi

  89. [101]

    A barrier method for contact avoiding particles in. J. Comput. Phys. , author =. 2024 , pages =. doi:10.1016/j.jcp.2023.112648 , language =

    2024 doi

  90. [102]

    Fast. J. Chem. Phys. , author =. 2021 , pages =. doi:10.1063/5.0044895 , abstract =

    2021 doi

  91. [103]

    1981 , author =

    Computer Simulation Using Particles , publisher =. 1981 , author =

    1981

  92. [104]

    Nestler, Franziska and Pippig, Michael and Potts, Daniel , title =. J. Comput. Phys. , volume =. 2015 , doi =

    2015

  93. [105]

    Science Advances , author =

    Interfacial gauge methods for incompressible fluid dynamics , volume =. Science Advances , author =. 2016 , pages =. doi:10.1126/sciadv.1501869 , abstract =

    2016 doi

  94. [106]

    BIT Numerical Mathematics , author =

    An accurate integral equation method for. BIT Numerical Mathematics , author =. 2021 , pages =. doi:10.1007/s10543-020-00816-1 , abstract =

    2021 doi

  95. [107]

    P. Int. J. Numer. Methods Fluids , keywords =. doi:10.1002/fld.4857 , file =

    doi

  96. [108]

    Arzneimittel-Forschung , author =

    [. Arzneimittel-Forschung , author =. 1975 , pmid =

    1975

  97. [109]

    On the. Appl. Comput. Harmon. Anal. , author =. 2012 , pages =. doi:10.1016/j.acha.2011.03.002 , abstract =

    2012 doi

  98. [110]

    BIT Numerical Mathematics , author =

    Singularity swap quadrature for nearly singular line integrals on closed curves in two dimensions , volume =. BIT Numerical Mathematics , author =. 2024 , pages =. doi:10.1007/s10543-024-01013-0 , abstract =

    2024 doi

  99. [111]

    A fast method for imposing periodic boundary conditions on arbitrarily-shaped lattices in two dimensions , volume =. J. Comput. Phys. , author =. 2023 , pages =. doi:10.1016/j.jcp.2022.111792 , language =

    2023 doi

  100. [112]

    International Journal of Multiphase Flow , author =

    Sedimentation of finite-size particles in quiescent wall-bounded shear-thinning and. International Journal of Multiphase Flow , author =. 2020 , pages =. doi:10.1016/j.ijmultiphaseflow.2020.103291 , language =

    2020 doi

  101. [113]

    A local target specific quadrature by expansion method for evaluation of layer potentials in. J. Comput. Phys. , author =. 2018 , pages =. doi:10.1016/j.jcp.2018.03.006 , language =

    2018 doi

  102. [114]

    A robust solver for elliptic. J. Comput. Phys. , author =. 2021 , pages =. doi:10.1016/j.jcp.2021.110511 , language =

    2021 doi

  103. [115]

    High-. SIAM J. Sci. Comput. , author =. 2022 , note =. doi:10.1137/21M1423051 , abstract =

    2022 doi

  104. [116]

    Adaptive. SIAM J. Sci. Comput. , author =. 2018 , pages =. doi:10.1137/17M1121615 , number =

    2018 doi

  105. [117]

    Error estimation for quadrature by expansion in layer potential evaluation , volume =. Adv. Comput. Math. , author =. 2017 , pages =. doi:10.1007/s10444-016-9484-x , abstract =

    2017 doi

  106. [118]

    arXiv:2208.10443v2 [math.NA] , author =

    Rapid evaluation of. arXiv:2208.10443v2 [math.NA] , author =. 2022 , note =

    2022

  107. [119]

    An. SIAM J. Sci. Comput. , author =. 1998 , keywords =. doi:10.1137/S1064827597317648 , number =

    1998 doi

  108. [120]

    Efficient methods for particle-resolved direct numerical simulation , isbn =

    Uhlmann, Markus and Derksen, Jos and Wachs, Anthony and Wang, Lian-Ping and Moriche, Manuel , year =. Efficient methods for particle-resolved direct numerical simulation , isbn =. Modeling. doi:10.1016/B978-0-32-390133-8.00013-X , pages =

    doi

  109. [121]

    REVIEWS ON ADVANCED MATERIALS SCIENCE , author =

    From passive to active sorting in microfluidics:. REVIEWS ON ADVANCED MATERIALS SCIENCE , author =. 2021 , pages =. doi:10.1515/rams-2020-0044 , abstract =

    2021 doi

  110. [122]

    A generalized. J. Chem. Phys. , author =. 2017 , pages =. doi:10.1063/1.4973842 , abstract =

    2017 doi

  111. [123]

    Spectrally accurate

    Sara Pålsson and Anna-Karin Tornberg , year=. Spectrally accurate. 1911.04875 , archivePrefix=

    1911

  112. [124]

    Ewald sums for. J. Chem. Phys. , author =. 2000 , pages =. doi:10.1063/1.1326477 , abstract =

    2000 doi

  113. [125]

    Osipov, Andrei and Rokhlin, Vladimir and Xiao, Hong , year =. Prolate

  114. [126]

    Solving integral equations on piecewise smooth boundaries using the

    Helsing, Johan , month = jan, year =. Solving integral equations on piecewise smooth boundaries using the. doi:10.48550/arXiv.1207.6737 , abstract =

    doi

  115. [127]

    ludvigak/

    Klinteberg, Ludvig af , month = oct, year =. ludvigak/

  116. [128]

    Kress, Rainer , year =. Linear

  117. [129]

    Geometric multivector analysis: from

    Rosén, Andreas and Dirac, Gabriel Andrew and Graßmann, Hermann , year =. Geometric multivector analysis: from

  118. [130]

    Calculus on manifolds: a modern approach to classical theorems of advanced calculus , isbn =

    Spivak, Michael , year =. Calculus on manifolds: a modern approach to classical theorems of advanced calculus , isbn =

  119. [131]

    Singularity swapping method for nearly singular integrals based on trapezoidal rule , url =

    Bao, Gang and Hua, Wenmao and Lai, Jun and Zhang, Jinrui , month = may, year =. Singularity swapping method for nearly singular integrals based on trapezoidal rule , url =

  120. [132]

    Fast adaptive high-order integral equation methods for electromagnetic scattering from smooth perfect electric conductors , url =

    Vico, Felipe and Greengard, Leslie and O'Neil, Michael and Rachh, Manas , month = jun, year =. Fast adaptive high-order integral equation methods for electromagnetic scattering from smooth perfect electric conductors , url =

  121. [133]

    Fast. Int. J. Numer. Methods Fluids. , author =. 2014 , pages =. doi:10.1002/fld.3953 , number =

    2014 doi

  122. [134]

    Berner, Julius and Grohs, Philipp and Kutyniok, Gitta and Petersen, Philipp , month = dec, year =. The. Mathematical. doi:10.1017/9781009025096.002 , note =

    doi

  123. [135]

    2023 , note =

    BIT Numerical Mathematics , author =. 2023 , note =. doi:10.1007/s10543-023-00959-x , abstract =

    2023 doi

  124. [136]

    BIT Numerical Mathematics , author =

    On the stability of unevenly spaced samples for interpolation and quadrature , volume =. BIT Numerical Mathematics , author =. 2023 , note =. doi:10.1007/s10543-023-00965-z , abstract =

    2023 doi

  125. [137]

    and Rahimian, Abtin and Stadler, Georg and Zorin, Denis , month = nov, year =

    Lu, Libin and Morse, Matthew J. and Rahimian, Abtin and Stadler, Georg and Zorin, Denis , month = nov, year =. Scalable simulation of realistic volume fraction red blood cell flows through vascular networks , isbn =. Proceedings of the. doi:10.1145/3295500.3356203 , abstract =

    doi

  126. [139]

    arXiv:2211.14537 [math.NA] , author =

    An. arXiv:2211.14537 [math.NA] , author =. 2022 , note =

    2022

  127. [140]

    Numerische Mathematik , author =

    Corrected trapezoidal rules for boundary integral equations in three dimensions , volume =. Numerische Mathematik , author =. 2021 , note =. doi:10.1007/s00211-021-01244-1 , abstract =

    2021 doi

  128. [141]

    Spectrally accurate solutions to inhomogeneous elliptic. J. Comput. Phys. , author =. 2022 , note =. doi:10.1016/j.jcp.2022.111594 , abstract =

    2022 doi

  129. [142]

    Immersed

    Stein, David B and Guy, Robert D and Thomases, Becca , month = apr, year =. Immersed. doi:10.1016/j.jcp.2017.01.010 , journal =

    2017 doi

  130. [143]

    , year =

    Fornari, Walter. , year =. Suspensions of finite-size rigid particles in laminar and turbulent flows , url =

  131. [144]

    Higher-order temporal integration for the incompressible. J. Comput. Phys. , author =. 2018 , note =. doi:10.1016/j.jcp.2018.08.054 , abstract =

    2018 doi

  132. [145]

    and Pic, Sylvie , month = nov, year =

    Guazzelli, Élisabeth and Morris, Jeffrey F. and Pic, Sylvie , month = nov, year =. A

  133. [146]

    An adaptive kernel-split quadrature method for parameter-dependent layer potentials , volume =. Adv. Comput. Math. , author =. 2022 , note =. doi:10.1007/s10444-022-09927-5 , abstract =

    2022 doi

  134. [147]

    IEEE Robotics and Automation Letters , author =

    Observability-. IEEE Robotics and Automation Letters , author =. 2023 , pages =. doi:10.1109/LRA.2023.3262176 , number =

    2023 doi

  135. [148]

    A fast, high-order scheme for evaluating volume potentials on complex. J. Comput. Phys. , author =. 2023 , note =. doi:10.1016/j.jcp.2022.111688 , abstract =

    2023 doi

  136. [149]

    SIAM Review , author =

    How. SIAM Review , author =. 2022 , keywords =. doi:10.1137/20M1336837 , number =

    2022 doi

  137. [150]

    Direct numerical simulation of finite sized particles settling for high

    Zaidi, Ali Abbas and Tsuji, Takuya and Tanaka, Toshitsugu , month = dec, year =. Direct numerical simulation of finite sized particles settling for high. doi:10.1016/j.ijheatfluidflow.2014.09.007 , journal =

    2014 doi

  138. [151]

    Sedimentation of finite-size spheres in quiescent and turbulent environments , volume =. J. Fluid Mech. , author =. 2016 , note =. doi:10.1017/jfm.2015.698 , abstract=

    2016 doi

  139. [152]

    A falling cloud of particles at a small but finite. J. Fluid Mech. , author =. 2011 , note =. doi:10.1017/S0022112010005501 , abstract =

    2011 doi

  140. [153]

    Dilute sedimenting suspensions of spheres at small inertia , volume =

    Bergougnoux, Laurence and Guazzelli, Élisabeth , month = may, year =. Dilute sedimenting suspensions of spheres at small inertia , volume =. doi:10.1017/jfm.2020.610 , journal =

    2020 doi

  141. [154]

    Sedimentation of small particles: how can such a simple problem be so difficult? , volume =. C. R. Mecanique , author =. 2006 , keywords =. doi:10.1016/j.crme.2006.07.009 , number =

    2006 doi

  142. [155]

    Computational methods for microfluidics , url =

    af Klinteberg, Ludvig , year =. Computational methods for microfluidics , url =

  143. [156]

    Computers & Mathematics with Applications , author =

    Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions , volume =. Computers & Mathematics with Applications , author =. 2022 , note =. doi:10.1016/j.camwa.2022.02.001 , abstract =

    2022 doi

  144. [157]

    International Journal for Numerical Methods in Fluids , author =

    Height functions for applying contact angles to. International Journal for Numerical Methods in Fluids , author =. 2009 , keywords =. doi:10.1002/fld.1974 , number =

    2009 doi

  145. [158]

    af Klinteberg, Ludvig and Askham, Travis , year =

  146. [159]

    A fast integral equation method for the two-dimensional

    af Klinteberg, Ludvig and Askham, Travis and Kropinski, Mary Catherine , month = may, year =. A fast integral equation method for the two-dimensional. doi:10.1016/j.jcp.2020.109353 , journal =

    2020 doi

  147. [160]

    BIT Numerical Mathematics , author =

    Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping , volume =. BIT Numerical Mathematics , author =. 2021 , pages =. doi:10.1007/s10543-020-00820-5 , abstract =

    2021 doi

  148. [161]

    A fast integral equation method for solid particles in viscous flow using quadrature by expansion , volume =

    af Klinteberg, Ludvig and Tornberg, Anna-Karin , month = dec, year =. A fast integral equation method for solid particles in viscous flow using quadrature by expansion , volume =. doi:10.1016/j.jcp.2016.09.006 , journal =

    2016 doi

  149. [162]

    Fast. Res. Math. Sci. , author =. 2017 , pages =. doi:10.1186/s40687-016-0092-7 , abstract =

    2017 doi

  150. [163]

    arXiv:1603.07467 [physics.flu-dyn] , author =

    Ewald summation for the rotlet singularity of. arXiv:1603.07467 [physics.flu-dyn] , author =. 2016 , note =

    2016 arXiv

  151. [164]

    Computers & Fluids , author =

    An explicit. Computers & Fluids , author =. 2014 , note =. doi:10.1016/j.compfluid.2014.05.029 , abstract =

    2014 doi

  152. [165]

    Corner singularities for elliptic problems:. J. Comput. Phys. , author =. 2008 , keywords =. doi:10.1016/j.jcp.2008.06.022 , abstract =

    2008 doi

  153. [166]

    Proceedings of the National Conference on Artificial Intelligence , author =

    Winning the. Proceedings of the National Conference on Artificial Intelligence , author =. 2006 , note =

    2006

  154. [167]

    arXiv , author =

    Computer vision for autonomous vehicles:. arXiv , author =. 2017 , note =

    2017

  155. [168]

    Journal of Field Robotics , author =

    Stanley:. Journal of Field Robotics , author =. 2006 , pages =. doi:10.1002/rob.20147 , abstract =

    2006 doi

  156. [169]

    Misra, Ishan and Girdhar, Rohit and Joulin, Armand , month = sep, year =. An

  157. [170]

    Carion, Nicolas and Massa, Francisco and Synnaeve, Gabriel and Usunier, Nicolas and Kirillov, Alexander and Zagoruyko, Sergey , month = may, year =. End-to-

  158. [171]

    On the evaluation of layer potentials close to their sources , volume =. J. Comput. Phys. , author =. 2008 , keywords =. doi:10.1016/j.jcp.2007.11.024 , abstract =

    2008 doi

  159. [172]

    Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators , volume =. Adv. Comput. Math. , author =. 2021 , pages =. doi:10.1007/s10444-021-09872-9 , abstract =

    2021 doi

  160. [173]

    Corrected trapezoidal rule for near-singular integrals in axi-symmetric. Adv. Comput. Math. , author =. 2022 , note =. doi:10.1007/s10444-022-09973-z , abstract =

    2022 doi

  161. [174]

    Proceedings of the National Academy of Sciences , author =

    Randomized algorithms for the low-rank approximation of matrices , volume =. Proceedings of the National Academy of Sciences , author =. 2007 , pmid =. doi:10.1073/pnas.0709640104 , abstract =

    2007 doi

  162. [175]

    Bit Numerical Mathematics , author =

    Spectral. Bit Numerical Mathematics , author =. 2000 , keywords =. doi:10.1023/A:1022338906936 , number =

    2000 doi

  163. [176]

    A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles , volume =. J. Fluid Mech. , author =. 2018 , note =. doi:10.1017/jfm.2017.836 , abstract =

    2018 doi

  164. [177]

    Computing with. SIAM J. Sci. Comput. , author =. 2017 , note =. doi:10.1137/16M1070207 , number =

    2017 doi

  165. [178]

    Numerical Methods for Partial Differential Equasion , author =

    Dynamic. Numerical Methods for Partial Differential Equasion , author =. 2007 , pmid =. doi:10.1002/num , abstract =

    2007 doi

  166. [181]

    Optimization of

    Wala, Matt and Klöckner, Andreas , month = nov, year =. Optimization of

  167. [182]

    A generalized traction integral equation for. J. Comput. Phys. , author =. 2016 , note =. doi:10.1016/j.jcp.2016.12.043 , number =

    2016 doi

  168. [183]

    Physics of Fluids A: Fluid Dynamics , author =

    A singularity method for unsteady linearized flow , volume =. Physics of Fluids A: Fluid Dynamics , author =. 1989 , note =. doi:10.1063/1.857329 , number =

    1989 doi

  169. [184]

    Hierarchical interpolative factorization for elliptic operators: differential equations , volume =. Commun. Pure Appl. Math. , author =. 2015 , note =

    2015

  170. [185]

    Mathematics of Computation , author =

    The. Mathematics of Computation , author =. 1964 , pages =. doi:10.2307/2003301 , number =

    1964 doi

  171. [186]

    Wang, Haiyong and Xiang, Shuhuang , year =. of

  172. [187]

    Communications in. Comm. App. Math and Comp. Sci. , author =. 2010 , note =

    2010

  173. [188]

    International Journal of Non-Linear Mechanics , author =

    A thermodynamic basis for the derivation of the. International Journal of Non-Linear Mechanics , author =. 2014 , note =. doi:10.1016/j.ijnonlinmec.2013.09.004 , abstract =

    2014 doi

  174. [189]

    arXiv , author =

    Conformal. arXiv , author =. 2016 , note =

    2016

  175. [190]

    Asymptotic analysis for close evaluation of layer potentials , volume =. J. Comput. Phys. , author =. 2018 , note =. doi:10.1016/j.jcp.2017.11.015 , abstract =

    2018 doi

  176. [191]

    IEEE Access , author =

    Extrinsic. IEEE Access , author =. 2019 , note =. doi:10.1109/ACCESS.2019.2937909 , abstract =

    2019 doi

  177. [192]

    Journal of Field Robotics , author =

    Automatic. Journal of Field Robotics , author =. 2015 , note =. doi:10.1002/rob.21542 , abstract =

    2015 doi

  178. [193]

    Extrinsic multi-sensor calibration for mobile robots using the

    Huang, Kaihong and Stachniss, Cyrill , month = sep, year =. Extrinsic multi-sensor calibration for mobile robots using the. 2017. doi:10.1109/IROS.2017.8205952 , abstract =

    2017 doi

  179. [194]

    On geometric models and their accuracy for extrinsic sensor calibration , isbn =

    Huang, Kaihong and Stachniss, Cyrill , month = sep, year =. On geometric models and their accuracy for extrinsic sensor calibration , isbn =. Proceedings -. doi:10.1109/ICRA.2018.8461029 , abstract =

    2018 doi

  180. [195]

    Dosovitskiy, Alexey and Beyer, Lucas and Kolesnikov, Alexander and Weissenborn, Dirk and Zhai, Xiaohua and Unterthiner, Thomas and Dehghani, Mostafa and Minderer, Matthias and Heigold, Georg and Gelly, Sylvain and Uszkoreit, Jakob and Houlsby, Neil , month = oct, year =. An

  181. [196]

    Targeted drug delivery by ultrasound-triggered margination of microbubbles , url =

    Guckenberger, Achim and Gekle, Stephan , year =. Targeted drug delivery by ultrasound-triggered margination of microbubbles , url =

  182. [197]

    doi:10.1109/IROS.2013.6696592 , abstract =

    Heng, Lionel and Li, Bo and Pollefeys, Marc , year =. doi:10.1109/IROS.2013.6696592 , abstract =

    2013 doi

  183. [198]

    Applied Optics , author =

    Accuracy of fish-eye lens models , volume =. Applied Optics , author =. 2010 , pages =. doi:10.1364/AO.49.003338 , abstract =

    2010 doi

  184. [199]

    Journal of Computational and Applied Mathematics , author =

    Estimates of the error in. Journal of Computational and Applied Mathematics , author =. 2011 , note =. doi:10.1016/j.cam.2011.09.019 , number =

    2011 doi

  185. [200]

    Optimization of fast algorithms for global. J. Comput. Phys. , author =. 2020 , note =. doi:10.1016/j.jcp.2019.108976 , abstract =

    2020 doi

  186. [201]

    Taylor states in stellarators:

    Malhotra, Dhairya and Cerfon, Antoine and Imbert-Gérard, Lise-Marie and O'Neil, Michael , month = nov, year =. Taylor states in stellarators:. doi:10.1016/j.jcp.2019.06.067 , journal =

    2019 doi

  187. [202]

    Abramowitz, Milton and Stegun, I. A. , year =. Handbook of

  188. [203]

    Physics of Plasmas , author =

    Three-dimensional codes to design stellarators , volume =. Physics of Plasmas , author =. 2002 , pages =. doi:10.1063/1.1419252 , number =

    2002 doi

  189. [204]

    arXiv:2001.09405 [math.NA] , author =

    Aliasing error of the exp\ (. arXiv:2001.09405 [math.NA] , author =. 2020 , note =

    2001

  190. [205]

    arXiv:1909.00049 [math.NA] , author =

    Solution of. arXiv:1909.00049 [math.NA] , author =. 2019 , note =

    1909

  191. [206]

    Mathematics of Computation , author =

    Method of lines transpose:. Mathematics of Computation , author =. 2014 , keywords =. doi:10.1090/S0025-5718-2014-02834-2 , abstract =

    2014 doi

  192. [207]

    Journal of Integral Equations and Applications , author =

    Rothe's. Journal of Integral Equations and Applications , author =. 1997 , pages =. doi:10.1216/jiea/1181075987 , number =

    1997 doi

  193. [208]

    Mountain, Rocky and Consortium, Mathematics , year =. Rocky

  194. [209]

    arXiv:1907.08537 [math.NA] , author =

    An integral equation based numerical method for the forced heat equation on complex domains , url =. arXiv:1907.08537 [math.NA] , author =. 2019 , note =

    1907 arXiv

  195. [210]

    Chemical Reviews , author =

    Electrostatic. Chemical Reviews , author =. 2018 , pages =. doi:10.1021/acs.chemrev.7b00305 , number =

    2018 doi

  196. [211]

    Boundary Value Problems , author =

    A quasi-reversibility regularization method for a. Boundary Value Problems , author =. 2019 , pages =. doi:10.1186/s13661-019-1142-z , abstract =

    2019 doi

  197. [212]

    Fast. Commun. Comput. Phys. , author =. 2015 , note =. doi:10.4208/cicp.181113.241014a , number =

    2015 doi

  198. [214]

    Modeling of

    Vorobjev, Yury N , editor =. Modeling of. Computational. 2019 , doi =

    2019

  199. [216]

    SIAM Rev

    Barycentric. SIAM Rev. , author =. 2004 , keywords =. doi:10.1137/S0036144502417715 , number =

    2004 doi

  200. [217]

    Variants of an explicit kernel-split panel-based. Adv. Comput. Math. , author =. 2015 , keywords =. doi:10.1007/s10444-014-9383-y , abstract =

    2015 doi

  201. [219]

    An accurate integral equation method for simulating multi-phase. J. Comput. Phys. , author =. 2015 , note =. doi:10.1016/j.jcp.2015.06.002 , abstract =

    2015 doi

  202. [220]

    Second kind integral equation formulation for the modified biharmonic equation and its applications , volume =. J. Comput. Phys. , author =. 2013 , note =. doi:10.1016/j.jcp.2013.04.034 , abstract =

    2013 doi

  203. [221]

    The boundary integral formulation of. J. Fluid Mech. , author =. 2018 , keywords =. doi:10.1017/jfm.2018.483 , abstract =

    2018 doi

  204. [222]

    arXiv:1901.11456 [math.AP] , author =

    Theoretical justification and error analysis for slender body theory with free ends , url =. arXiv:1901.11456 [math.AP] , author =. 2019 , note =

    1901

  205. [223]

    arXiv:1807.00178 [math.AP] , author =

    Theoretical justification and error analysis for slender body theory , url =. arXiv:1807.00178 [math.AP] , author =. 2018 , note =

    2018 arXiv

  206. [224]

    Simulating the dynamics and interactions of flexible fibers in. J. Comput. Phys. , author =. 2004 , pages =. doi:10.1016/j.jcp.2003.10.017 , abstract =

    2004 doi

  207. [225]

    2002 , pages =

    The American Mathematical Monthly , author =. 2002 , pages =. doi:10.2307/2695765 , number =

    2002 doi

  208. [226]

    Regularized. J. Comput. Phys. , author =. 2018 , note =. doi:10.1016/j.jcp.2018.08.055 , abstract =

    2018 doi

  209. [227]

    A three-dimensional model of flagellar swimming in a. J. Fluid Mech. , author =. 2019 , note =. doi:10.1017/jfm.2019.36 , abstract =

    2019 doi

  210. [228]

    Computation of three-dimensional. J. Comput. Phys. , author =. 2010 , note =. doi:10.1016/j.jcp.2010.06.012 , abstract =

    2010 doi

  211. [229]

    Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensions , url =

    Wang, Jun and Greengard, Leslie , month = mar, year =. Hybrid asymptotic/numerical methods for the evaluation of layer heat potentials in two dimensions , url =

  212. [230]

    Computers & Fluids , author =

    A fast method to compute triply-periodic. Computers & Fluids , author =. 2016 , note =. doi:10.1016/j.compfluid.2016.04.007 , abstract =

    2016 doi

  213. [231]

    Journal of Computational and Applied Mathematics , author =

    The method of steepest descent for estimating quadrature errors , volume =. Journal of Computational and Applied Mathematics , author =. doi:10.1016/j.cam.2016.02.028 , abstract =

    2016 doi

  214. [232]

    SIAM Journal on Applied Mathematics , author =

    On. SIAM Journal on Applied Mathematics , author =. 2009 , keywords =. doi:10.1137/070698154 , number =

    2009 doi

  215. [233]

    Clenshaw-. SIAM J. Sci. Comput. , author =. 2008 , keywords =. doi:10.1137/07070200X , number =

    2008 doi

  216. [234]

    On the accurate evaluation of unsteady

    Greengard, Leslie and Jiang, Shidong and Wang, Jun , month = nov, year =. On the accurate evaluation of unsteady

  217. [235]

    A fast algorithm for. J. Comput. Phys. , author =. 2019 , pages =. doi:10.1016/j.jcp.2019.03.024 , abstract =

    2019 doi

  218. [236]

    and Epstein, Charles L and Greengard, Leslie and Jiang, Shidong and Wang, Jun , month = feb, year =

    Barnett, Alex H. and Epstein, Charles L and Greengard, Leslie and Jiang, Shidong and Wang, Jun , month = feb, year =. Explicit unconditionally stable methods for the heat equation via potential theory , url =

  219. [237]

    Machine learning acceleration of simulations of

    Kabacaoglu, Gokberk and Biros, George , month = mar, year =. Machine learning acceleration of simulations of

  220. [238]

    Fast integral equation methods for the modified. J. Comput. Phys. , author =. 2011 , note =. doi:10.1016/j.jcp.2010.09.030 , abstract =

    2011 doi

  221. [239]

    Computers & Mathematics with Applications , author =

    Fast integral equation methods for. Computers & Mathematics with Applications , author =. 2011 , note =. doi:10.1016/j.camwa.2011.02.024 , abstract =

    2011 doi

  222. [240]

    Simulation and validation of surfactant-laden drops in two-dimensional. J. Comput. Phys. , author =. 2019 , note =. doi:10.1016/j.jcp.2018.12.044 , abstract =

    2019 doi

  223. [242]

    BIT Numerical Mathematics , author =

    Fast computation of eigenvalues of companion, comrade, and related matrices , volume =. BIT Numerical Mathematics , author =. 2014 , keywords =. doi:10.1007/s10543-013-0449-x , abstract =

    2014 doi

  224. [243]

    Stability and convergence of the method of fundamental solutions for. J. Comput. Phys. , author =. 2008 , note =. doi:10.1016/j.jcp.2008.04.008 , abstract =

    2008 doi

  225. [244]

    Brinkman, H. C. , month = dec, year =. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles , volume =. doi:10.1007/BF02120313 , journal =

    doi

  226. [245]

    Computer Methods in Applied Mechanics and Engineering , author =

    A versatile algorithm for the treatment of open boundary conditions in. Computer Methods in Applied Mechanics and Engineering , author =. 2018 , keywords =. doi:10.1016/j.cma.2018.08.004 , abstract =

    2018 doi

  227. [246]

    and Johnston, Peter R , month = may, year =

    Elliott, David and Johnston, Barbara M. and Johnston, Peter R , month = may, year =. A complete error analysis for the evaluation of a two-dimensional nearly singular boundary element integral , volume =. doi:10.1016/j.cam.2014.11.015 , journal =

    2014 doi

  228. [247]

    Computers & Fluids , author =

    The. Computers & Fluids , author =. 2006 , pages =. doi:10.1016/j.compfluid.2004.12.004 , number =

    2006 doi

  229. [248]

    High-. J. Comput. Phys. , author =. 1982 , pages =. doi:10.1016/0021-9991(82)90058-4 , number =

    1982 doi

  230. [249]

    Computers & Fluids , author =

    Benchmark spectral results on the lid-driven cavity flow , volume =. Computers & Fluids , author =. 1998 , pages =. doi:10.1016/S0045-7930(98)00002-4 , number =

    1998 doi

  231. [250]

    Gopal, Abinand and Trefethen, Lloyd N , note =. New

  232. [251]

    SIAM Review , author =

    Finding. SIAM Review , author =. 2011 , keywords =. doi:10.1137/090771806 , number =

    2011 doi

  233. [252]

    Acheson, D. J. , year =. Elementary

  234. [253]

    , month = jan, year =

    Higham, Nicholas J. , month = jan, year =. Accuracy and

  235. [254]

    An overview of projection methods for incompressible flows , volume =. Comput. Meth. Appl. Mech. Eng. , author =. 2006 , pages =. doi:10.1016/j.cma.2005.10.010 , abstract =

    2006 doi

  236. [255]

    An adaptive fast

    Wang, Jun and Greengard, Leslie , year =. An adaptive fast

  237. [257]

    An. SIAM J. Sci. Comput. , author =. 2018 , keywords =. doi:10.1137/17M1159865 , abstract =

    2018 doi

  238. [258]

    A new mixed potential representation for the equations of unsteady, incompressible flow , url =

    Greengard, Leslie and Jiang, Shidong , month = sep, year =. A new mixed potential representation for the equations of unsteady, incompressible flow , url =

  239. [259]

    Direct evaluation of hyper-singularity in surface integral equation using quadrature by expansion , isbn =

    Peng, Shao-xin and Lee, Jin-fa , month = jun, year =. Direct evaluation of hyper-singularity in surface integral equation using quadrature by expansion , isbn =. doi:10.1109/APS.2016.7695859 , booktitle =

    2016 doi

  240. [260]

    SIAM Review , author =

    Accelerating the. SIAM Review , author =. 2004 , note =. doi:10.1137/S003614450343200X , abstract =

    2004 doi

  241. [261]

    The type 3 nonuniform. J. Comput. Phys. , author =. 2005 , pmid =. doi:10.1016/j.jcp.2004.12.004 , abstract =

    2005 doi

  242. [262]

    Fast and. SIAM J. Sci. Comput. , author =. 2014 , note =. doi:10.1137/130945582 , number =

    2014 doi

  243. [263]

    Mathematics of Computation , author =

    On the convergence rates of. Mathematics of Computation , author =. 2011 , keywords =. doi:10.1090/S0025-5718-2011-02549-4 , number =

    2011 doi

  244. [264]

    Krylov deferred correction accelerated method of lines transpose for parabolic problems , volume =. J. Comput. Phys. , author =. 2008 , keywords =. doi:10.1016/j.jcp.2007.09.018 , abstract =

    2008 doi

  245. [265]

    A fast direct solver for boundary value problems on locally perturbed geometries , volume =. J. Comput. Phys. , author =. 2018 , note =. doi:10.1016/j.jcp.2017.12.013 , abstract =

    2018 doi

  246. [266]

    and Higham, Desmond J

    Higham, Catherine F. and Higham, Desmond J. , year =. Deep

  247. [267]

    Shamshirgar, Davood Saffar and Tornberg, Anna-karin , note =. Fast

  248. [268]

    Spectral accuracy in fast. J. Comput. Phys. , author =. 2011 , keywords =. doi:10.1016/j.jcp.2011.08.022 , abstract =

    2011 doi

  249. [269]

    Journal of Scientific Computing , author =

    A. Journal of Scientific Computing , author =. 2018 , note =. doi:10.1007/s10915-018-0679-9 , number =

    2018 doi

  250. [270]

    Stable. SIAM J. Sci. Comput. , author =. 2011 , note =. doi:10.1137/09076756X , number =

    2011 doi

  251. [271]

    SIAM Rev

    Julia:. SIAM Rev. , author =. 2017 , keywords =. doi:10.1137/141000671 , abstract =

    2017 doi

  252. [272]

    Acta Numerica , author =

    The immersed boundary method , volume =. Acta Numerica , author =. 2002 , note =. doi:10.1017/S0962492902000077 , abstract =

    2002 doi

  253. [273]

    Larsson, Elisabeth , year =

  254. [274]

    Partition of unity extension of functions on complex domains , volume =. J. Comput. Phys. , author =. 2018 , note =. doi:10.1016/j.jcp.2018.08.012 , abstract =

    2018 doi

  255. [275]

    Gimbutas, Zydrunas and Greengard, Leslie , year =

  256. [276]

    Mathematics of

    Vidal, Rene and Bruna, Joan and Giryes, Raja and Soatto, Stefano , month = dec, year =. Mathematics of

  257. [277]

    Communications in Mathematical Sciences , author =

    Semi-implicit spectral deferred correction methods for ordinary differential equations , volume =. Communications in Mathematical Sciences , author =. 2003 , note =. doi:10.4310/CMS.2003.v1.n3.a6 , abstract =

    2003 doi

  258. [278]

    A. SIAM J. Sci. Comput. , author =. 2016 , keywords =. doi:10.1137/15M1043066 , number =

    2016 doi

  259. [279]

    Adaptive time stepping for vesicle suspensions , volume =. J. Comput. Phys. , author =. 2016 , note =. doi:10.1016/j.jcp.2015.11.050 , abstract =

    2016 doi

  260. [280]

    An adaptive fast multipole accelerated. J. Comput. Phys. , author =. 2017 , note =. doi:10.1016/j.jcp.2017.04.063 , abstract =

    2017 doi

  261. [281]

    Wala, Matt and Klöckner, Andreas , month = jan, year =. A

  262. [282]

    and Turc, Catalin , month = nov, year =

    Pérez-Arancibia, Carlos and Faria, Luiz M. and Turc, Catalin , month = nov, year =. Harmonic density interpolation methods for high-order evaluation of

  263. [283]

    SIAM Journal on Numerical Analysis , author =

    Implicit-. SIAM Journal on Numerical Analysis , author =. 1995 , note =. doi:10.1137/0732037 , abstract =

    1995 doi

  264. [284]

    A multiblob approach to colloidal hydrodynamics with inherent lubrication , volume =. J. Chem. Phys. , author =. 2014 , pmid =. doi:10.1063/1.4901889 , abstract =

    2014 doi

  265. [285]

    Multiscale Modeling & Simulation , author =

    Staggered. Multiscale Modeling & Simulation , author =. 2012 , keywords =. doi:10.1137/120864520 , number =

    2012 doi

  266. [286]

    Pairwise hydrodynamic interactions of vesicles in uniform electric fields , url =

    Wu, Bowei and Veerapaneni, Shravan , year =. Pairwise hydrodynamic interactions of vesicles in uniform electric fields , url =

  267. [287]

    Integral equation methods for the heat equation in moving geometry by , number =

    Wang, Jun , year =. Integral equation methods for the heat equation in moving geometry by , number =

  268. [288]

    Universal image systems for non-periodic and periodic

    Yan, Wen and Shelley, Michael , year =. Universal image systems for non-periodic and periodic

  269. [289]

    Flexibly imposing periodicity in kernel independent. J. Comput. Phys. , author =. 2018 , keywords =. doi:10.1016/j.jcp.2017.11.012 , abstract =

    2018 doi

  270. [290]

    Fast. Appl. Comput. Harmon. Anal. , author =. 1995 , pages =. doi:10.1006/acha.1995.1007 , number =

    1995 doi

  271. [291]

    Fast. SIAM J. Sci. Comput. , author =. 1993 , note =. doi:10.1137/0914081 , number =

    1993 doi

  272. [292]

    An integral equation formulation for rigid bodies in. J. Comput. Phys. , author =. 2017 , pages =. doi:10.1016/j.jcp.2016.12.018 , abstract =

    2017 doi

  273. [293]

    Immersed boundary smooth extension:

    Stein, David B and Guy, Robert D and Thomases, Becca , month = jan, year =. Immersed boundary smooth extension:. doi:10.1016/j.jcp.2015.10.023 , journal =

    2015 doi

  274. [294]

    A boundary-integral framework to simulate viscous erosion of a porous medium , abstract =

    Quaife, Bryan D and Nicholas, M and Moore, J , year =. A boundary-integral framework to simulate viscous erosion of a porous medium , abstract =

  275. [295]

    and Klöckner, Andreas and Olson, Luke N

    Beams, Natalie N. and Klöckner, Andreas and Olson, Luke N. , month = apr, year =. High-order

  276. [296]

    Computers & Mathematics with Applications , author =

    Numerical quadratures for singular and hypersingular integrals , volume =. Computers & Mathematics with Applications , author =. 2001 , keywords =. doi:10.1016/S0898-1221(00)00277-7 , abstract =

    2001 doi

  277. [297]

    Mathematics of Computation , author =

    Solution of. Mathematics of Computation , author =. 1970 , keywords =. doi:10.2307/2004623 , abstract =

    1970 doi

  278. [298]

    A fast direct solver for boundary integral equations in two dimensions , volume =. J. Comput. Phys. , author =. 2005 , pages =. doi:10.1016/j.jcp.2004.10.033 , number =

    2005 doi

  279. [299]

    Frontiers of Mathematics in China , author =

    A direct solver with. Frontiers of Mathematics in China , author =. 2012 , keywords =. doi:10.1007/s11464-012-0188-3 , number =

    2012 doi

  280. [300]

    SIAM Journal on Matrix Analysis and Applications , author =

    Fast and. SIAM Journal on Matrix Analysis and Applications , author =. 2015 , note =. doi:10.1137/140983434 , number =

    2015 doi

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