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Paper Citation Record · LEDGER

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow

As of 13 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 0 inbound Pith citation observations for arXiv:2412.08355.

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pith.paper-citation-record.v1
2412.08355 v1

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measured 53 of 53 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Source: cited_works

Reference resolution

53 of 53 outbound references displayed

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External citation measurements

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Outbound references

Observation d429864e-4436-43f6-9c40-2e0300b3cd89 · outbound

This paper cites A convergence analysis of generalized multiscale finite element methods.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow A convergence analysis of generalized multiscale finite element methods

Reference 1

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Observation 384fe69a-8895-46fd-af5b-d1961ca02b06 · outbound

This paper cites Multiscale model reduction for shale gas transport in poroelastic fractured media.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multiscale model reduction for shale gas transport in poroelastic fractured media

Reference 2

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This paper cites Multiscale model reduction for shale gas trans- port in fractured media.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multiscale model reduction for shale gas trans- port in fractured media

Reference 3

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This paper cites Pyamg: Algebraic multigrid solvers in python.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Pyamg: Algebraic multigrid solvers in python

Reference 4

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This paper cites Pyamg: algebraic multigrid solvers in python.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Pyamg: algebraic multigrid solvers in python

Reference 5

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This paper cites The Mixed Virtual Element Discretization for highly-anisotropic problems: the role of the boundary degrees of freedom.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow The Mixed Virtual Element Discretization for highly-anisotropic problems: the role of the boundary degrees of freedom

Reference 6

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Observation bab90c12-bf9c-43d5-8a02-a8fee2ef56a4 · outbound

This paper cites Algebraic distance for anisotropic diffusion problems: multilevel results.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Algebraic distance for anisotropic diffusion problems: multilevel results

Reference 7

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Observation 642776f5-b8d1-45fd-956f-7a9c32741667 · outbound

This paper cites Smoothed aggregation spectral element agglomeration amg: Sa- ρ amge.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Smoothed aggregation spectral element agglomeration amg: Sa- ρ amge

Reference 8

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This paper cites Briggs, Van Emden Henson, and Steve F.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Briggs, Van Emden Henson, and Steve F

Reference 9

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This paper cites First order hyper- bolic approach for anisotropic diffusion equation.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow First order hyper- bolic approach for anisotropic diffusion equation

Reference 10

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This paper cites Spectral amge (ρ amge).

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Spectral amge (ρ amge)

Reference 11

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Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Spectral element agglomerate amge

Reference 12

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This paper cites Constraint energy minimizing general- ized multiscale finite element method.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Constraint energy minimizing general- ized multiscale finite element method

Reference 13

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Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Non-local multi-continua upscaling for flows in heterogeneous fractured media

Reference 14

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This paper cites Generalized multiscale finite el- ement methods for problems in perforated heterogeneous domains.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Generalized multiscale finite el- ement methods for problems in perforated heterogeneous domains

Reference 15

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This paper cites Multiscale model reduction for transport and flow problems in perforated domains.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multiscale model reduction for transport and flow problems in perforated domains

Reference 16

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This paper cites Generalized multiscale finite element methods (gmsfem).

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Generalized multiscale finite element methods (gmsfem)

Reference 17

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This paper cites Multiscale spectral amge solvers for high-contrast flow problems.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multiscale spectral amge solvers for high-contrast flow problems

Reference 18

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This paper cites Multiscale finite element methods for high-contrast problems using local spectral basis functions.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multiscale finite element methods for high-contrast problems using local spectral basis functions

Reference 19

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Observation f5d9b9f8-7f30-4c2e-a451-ecc5443477df · outbound

This paper cites On two-grid convergence esti- mates.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow On two-grid convergence esti- mates

Reference 20

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Observation abe22ec9-65c8-4d73-acbc-87de4b1a0c01 · outbound

This paper cites Domain decomposition preconditioners for multiscale flows in high-contrast media.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Domain decomposition preconditioners for multiscale flows in high-contrast media

Reference 21

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Observation 8a3e6593-b1d1-460d-9328-93b64858d3c6 · outbound

This paper cites A new smoothed aggregation multigrid method for anisotropic problems.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow A new smoothed aggregation multigrid method for anisotropic problems

Reference 22

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This paper cites Gmsh: A 3-d finite element mesh generator with built-in pre-and post-processing facilities.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Gmsh: A 3-d finite element mesh generator with built-in pre-and post-processing facilities

Reference 23

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This paper cites A high-order non field-aligned approach for the discretization of strongly anisotropic diffusion operators in magnetic fusion.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow A high-order non field-aligned approach for the discretization of strongly anisotropic diffusion operators in magnetic fusion

Reference 24

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This paper cites An efficient high-order numerical solver for diffusion equations with strong anisotropy.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow An efficient high-order numerical solver for diffusion equations with strong anisotropy

Reference 25

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This paper cites Finite element and higher order difference for- mulations for modelling heat transport in magnetised plasmas.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Finite element and higher order difference for- mulations for modelling heat transport in magnetised plasmas

Reference 26

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This paper cites A constrained finite element method sat- isfying the discrete maximum principle for anisotropic diffusion problems.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow A constrained finite element method sat- isfying the discrete maximum principle for anisotropic diffusion problems

Reference 27

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Observation 948f9def-2092-4b73-9c74-295a2afa4f5d · outbound

This paper cites Automated solution of differential equations by the finite element method: The FEniCS book , volume 84.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Automated solution of differential equations by the finite element method: The FEniCS book , volume 84

Reference 28

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Observation 68b47072-1b2c-4a1d-85d3-f522b434f5a1 · outbound

This paper cites Nonsymmetric reduction-based algebraic multigrid.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Nonsymmetric reduction-based algebraic multigrid

Reference 29

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Observation e212ba76-7a2e-456d-a14e-c82917457e6e · outbound

This paper cites A root-node–based algebraic multigrid method.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow A root-node–based algebraic multigrid method

Reference 30

Resolution
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Observation e01a977f-af31-4cba-8b78-8b0a0bc87cb1 · outbound

This paper cites Nonsymmetric algebraic multigrid based on local approximate ideal restriction (lAIR).

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Nonsymmetric algebraic multigrid based on local approximate ideal restriction (lAIR)

Reference 31

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Observation 0192685f-d48b-4efd-88d0-e45f8af91dac · outbound

This paper cites Convergence in norm of nonsymmetric algebraic multigrid.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Convergence in norm of nonsymmetric algebraic multigrid

Reference 32

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This paper cites The partition of unity finite element method: basic theory and applications.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow The partition of unity finite element method: basic theory and applications

Reference 33

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Observation c304bcb6-2207-4eda-b80f-042dcdad1d9f · outbound

This paper cites Convergence analysis of perturbed two-grid and multigrid methods.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Convergence analysis of perturbed two-grid and multigrid methods

Reference 34

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verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.233038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.847147Z digest=sha256:3fe3d4bc56fddc38e7ea24dac0f7d17dfaa5efda56b527a006d2bb25ec9870e5

Observation 8ffd6b98-1d24-4277-b2c7-2a21fa8024e1 · outbound

This paper cites Algebraic multigrid.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Algebraic multigrid

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.219976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.850756Z digest=sha256:0cc3872ec56b9ae69510929b67c4230257a6d461e2a8d043bb6255f107d770b8

Observation 405259fb-e263-4408-b995-5345cd4bf22a · outbound

This paper cites Smoothed aggregation solvers for anisotropic diffusion.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Smoothed aggregation solvers for anisotropic diffusion

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.204184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.854566Z digest=sha256:b63dfc94dd1dc2fe9bbd2f6f3fd3ab767f52f1738c4d1acaf6602f97174cdc77

Observation 5af0092a-b9c7-4822-9bb0-493201544722 · outbound

This paper cites Preserving monotonicity in anisotropic diffusion.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Preserving monotonicity in anisotropic diffusion

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.191723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.859030Z digest=sha256:5a8dc17eef50ebc99a2ce8b56ca5a533fa8c81bf66f3954f52fa811109ee17f0

Observation 4226b935-7eee-4ca1-ba1f-229f2ba381d6 · outbound

This paper cites Air algebraic multigrid for a space- time hybridizable discontinuous galerkin discretization of advection (-diffusion).

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Air algebraic multigrid for a space- time hybridizable discontinuous galerkin discretization of advection (-diffusion)

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.179141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.862849Z digest=sha256:a86d563d3c94023d26bf60aa9e7ab844469a0097b2c1e70f364ab6da20864c98

Observation dca0b300-916c-4c6c-9a4a-c5c70e7f7e15 · outbound

This paper cites Nonlinear magnetohydrodynamics simulation using high- order finite elements.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Nonlinear magnetohydrodynamics simulation using high- order finite elements

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.167107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.866583Z digest=sha256:9dd669eea1141c0452acb0b1a9c989115010a5df8986bc92ce2abeb749c6e98e

Observation 7de92fdc-0376-4b82-ab6a-c16d3446449c · outbound

This paper cites Multigrid.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multigrid

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.154980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.870414Z digest=sha256:dcccc5bf62513278fa46d0f746dbaa58ed91c10ee6f6c901bbbc1b541b637c08

Observation 26e6caa7-1cba-4eaf-9a16-65b26033b5ab · outbound

This paper cites Generalized multiscale finite element method for discrete network (graph) models.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Generalized multiscale finite element method for discrete network (graph) models

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.143201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.874063Z digest=sha256:7d62ef27861f8fcb0af720ca9b011c60d5e0014aa24db84a873ab9dd04cd439b

Observation c8b5bff4-0319-4d1b-8650-113a6bb7c0f3 · outbound

This paper cites Multiscale dimension reduction for flow and transport problems in thin domain with reactive boundaries.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multiscale dimension reduction for flow and transport problems in thin domain with reactive boundaries

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.130350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.877862Z digest=sha256:848cf9ea7f715319c6d058ddde67c60c98ee309d5772186087c484d2dd991e56

Observation 5817c25a-0c42-4941-9753-032818e81a3d · outbound

This paper cites Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.114451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.881624Z digest=sha256:14f25e7590d6740d3db8d06869e86a4360c1679d6aa8af4beeffb613b6904f50

Observation 49dd1537-98d1-4e43-9a94-57562ffcc080 · outbound

This paper cites Decoupled multiscale numerical approach for reactive transport in marine sediment column.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Decoupled multiscale numerical approach for reactive transport in marine sediment column

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.101185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.885676Z digest=sha256:a7c6bdf0b93eed89f4a708602dd1e2532927cee23ae2fa641c881e0fde9a12e6

Observation e878089a-39d2-401e-ba74-62214dd68e3f · outbound

This paper cites Multiscale model reduction for pore- scale simulation of li-ion batteries using gmsfem.Journal of Computational and Applied Mathematics, 344:73–88, 2018.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multiscale model reduction for pore- scale simulation of li-ion batteries using gmsfem.Journal of Computational and Applied Mathematics, 344:73–88, 2018

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.088123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.890024Z digest=sha256:9d07703b7b28bfa2533589a3774d0d6b039ac2f36f5382b9f021e5d678876153

Observation ff86423b-07ff-402a-a5e0-71558104756e · outbound

This paper cites An adaptive two-grid preconditioner and linearly implicit scheme for shale gas transport in fractured porous media.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow An adaptive two-grid preconditioner and linearly implicit scheme for shale gas transport in fractured porous media

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-11T18:06:12.893869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T18:06:12.893869Z digest=sha256:3757a233f11ae489f54a6c6daec0f664af1ef9ab9e01ccdd349c15aca702eb10

Observation 97237c70-2664-4a88-826a-555eccc169c1 · outbound

This paper cites Multilevel block factorization preconditioners: Matrix-based analysis and algorithms for solving finite element equations.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Multilevel block factorization preconditioners: Matrix-based analysis and algorithms for solving finite element equations

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.075796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.898077Z digest=sha256:5a7f61f0d8d5ac4b729123b62fe360c5e9b6a7be27dad86fa9336168eb8178f4

Observation 3b2e985f-b110-4792-9f95-1d7f35401fa1 · outbound

This paper cites Coarse spaces by algebraic multigrid: Multigrid convergence and upscaling error estimates.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Coarse spaces by algebraic multigrid: Multigrid convergence and upscaling error estimates

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.063088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.901658Z digest=sha256:52e6abfade5d6bae47a1497d3e2284bd0df47c40c5ad29214d898ce42a1fc2a8

Observation 1264d891-b629-4041-ad7c-70a6b74afbce · outbound

This paper cites Scipy 1.0: fundamental algorithms for scientific computing in python.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Scipy 1.0: fundamental algorithms for scientific computing in python

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.050474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.905370Z digest=sha256:f239ec868774f7791db5608b454ea238f7340a613da55dfa56f9735d87dca7bc

Observation baba16b1-9261-4723-8d2a-15222e0eed02 · outbound

This paper cites A fast algebraic multigrid solver and accurate discretization for highly anisotropic heat flux i: open field lines.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow A fast algebraic multigrid solver and accurate discretization for highly anisotropic heat flux i: open field lines

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.037491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.909053Z digest=sha256:18ec8321a32352004feb994d7d7c50747ad5fed61243f09df0b26fb6a4b78162

Observation 940b9087-a6fa-4faa-807d-e07efb80414e · outbound

This paper cites An accurate SUPG- stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow An accurate SUPG- stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.024503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.913437Z digest=sha256:ef6c4832117a875f598c97ff6882a0a4fe9adbdbae16c7a76ad7ddc2214e37ac

Observation d442e9cb-f5d5-4814-927e-742c674f41f9 · outbound

This paper cites The method of alternating projections and the method of sub- space corrections in hilbert space.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow The method of alternating projections and the method of sub- space corrections in hilbert space

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:13.011748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.917578Z digest=sha256:94ef7a4b745fad401a6ffea8e199af35cb4f7b587002781e3491cc086bfbbae2

Observation bf12ff09-0f68-4705-a5c9-ecd9128c51d8 · outbound

This paper cites Algebraic multigrid methods.

Multiscale approximation and two-grid preconditioner for extremely anisotropic heat flow Algebraic multigrid methods

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:06:12.998959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T18:06:12.921613Z digest=sha256:4ebbe9d9c8146c3ce22035e372f3f5e6270138ec62ab21c82516aa43ae886e33

Pith citing papers

No inbound Pith citation observations are available.