CK-MPM: A Compact-Kernel Material Point Method

Michael Liu; Minchen Li; Xinlei Wang

REVIEW 4 major objections 6 minor 8 references

CK-MPM: A Compact-Kernel Material Point Method

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A compact, twice-differentiable kernel run on two quarter-cell-shifted grids gives material-point simulations the stability of quadratic B-splines at near-linear cost.

desk verdict Genuinely novel dual-grid compact kernel, but a broken G2P equation and an invalid proof step as printed mean the conservation claims need correction before this is citable. read the letter →

arxiv 2412.10399 v4 pith:5EWGQZVL submitted 2024-12-04 cs.GR physics.comp-ph

Michael Liu , Xinlei Wang , Minchen Li This is my paper · ORCID

classification cs.GRphysics.comp-ph MSC 65M7565D07

keywords materialpointmethodcompactkerneldualgridcell-crossinginstabilityaffineparticle-in-cellnumericaldiffusionmomentumconservationfracturesimulation

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 claims that a single compact kernel, $K_1(x) = 1 - |x| + \frac{1}{2\pi}\sin(2\pi|x|)$, evaluated on two grids shifted by $\pm\frac14\Delta x$, can replace quadratic B-spline interpolation in the material point method. This removes cell-crossing instability while keeping the transfer stencil at 16 grid nodes per particle in three dimensions, between the 8 nodes of linear kernels and the 27 of quadratic B-splines. The paper further claims that, with Affine Particle-In-Cell (APIC) transfer, the scheme conserves linear and angular momentum, runs faster than quadratic B-spline MPM, and loses less energy on high-frequency motions. A careful reader would care because these are the standard objections to smooth MPM kernels — cost, diffusion, and implementation complexity — and the paper addresses all three at once.

What carries the argument

The load-bearing object is the kernel $K_1(x) = 1 - |x| + \frac{1}{2\pi}\sin(2\pi|x|)$ together with its evaluation on two grids shifted by $\pm \Delta x/4$. The sine term smooths the tent at $x=0$ and at $|x|=1$, giving $C^2$ continuity, while the identity $K_1(x) + K_1(1-x) = 1$ preserves normalization. First-order accuracy is restored because the offset makes the sine arguments on the two grids differ by $\pi$, so the sine contributions cancel and the tent contributions reproduce linear polynomials. The momentum-conservation proofs lean on this linear-reproduction property, since both particle-to-grid and grid-to-particle transfers reduce to weighted averages over the two grids.

What would settle it

Evaluate the linear-reproduction identity (Eq. 10) at a particle position using grid offsets of $+0.26\Delta x$ and $-0.26\Delta x$ instead of $\pm 0.25\Delta x$; the sine arguments no longer differ by $\pi$, the cancellation fails, and the weighted sum of node positions will miss the particle position by an amount proportional to the offset error, showing that first-order accuracy is tied to the exact quarter-cell shift.

Watch

Extended reading notes

Core claim

The central discovery is that a twice-continuously differentiable kernel need not pay the usual support penalty. The kernel $K_1(x) = 1 - |x| + \frac{1}{2\pi}\sin(2\pi|x|)$ is the linear tent plus a single sine term; it is non-negative, normalized, compactly supported on one cell, and satisfies the partition-of-unity identity $K_1(x) + K_1(1-x) = 1$. On one grid this kernel does not reproduce linear functions, so the paper evaluates it on two staggered grids offset by $\pm\Delta x/4$. At that specific offset the sine terms on the two grids are opposite in phase and cancel exactly, restoring first-order accuracy while every particle touches only the 16 nodes of the two cells it occupies. The paper shows that this construction can drive standard particle-in-cell (PIC), Affine Particle-In-Cell (APIC), and Moving Least Squares (MLS) MPM transfers, and that the APIC variant conserves both linear and angular momentum.

Load-bearing premise

The scheme's first-order accuracy rests entirely on the two staggered grids being offset by exactly one quarter of a grid spacing; any other offset breaks the phase cancellation of the sine terms and with it the linear-reproduction property.

Editorial extensions

If this is right

The two-sphere collision test keeps total linear momentum to about $10^{-5}$ relative error, and the rotating-rod test keeps total angular momentum to about $6 \times 10^{-3}$ relative error, over five simulated seconds.
The 16-node stencil cuts particle-grid transfer work by 40 percent relative to quadratic B-splines; the paper reports roughly 10 percent faster fused GPU transfer kernels and about 1.5 times faster standard transfers, with grid memory doubled.
In the contact test, a ball with a $1.5\Delta x$ gap to a cylinder wall falls and bounces freely with the compact kernel, while the same setup with quadratic B-spline MPM leaves the ball stuck.
The compact kernel preserves high-frequency velocity modes noticeably longer, showing slower kinetic- and total-energy decay than quadratic B-spline MPM in the oscillating cuboid test.
Materials modeled with the compact kernel fracture more readily under impact; using 27 particles per cell instead of 8 suppresses these unwanted fractures in the twisting-bar test.

Reading between the lines

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

The exact $\pm\Delta x/4$ offset is a hidden implementation constraint: if block-boundary handling or a simplified kernel drifts from it, the sine cancellation fails and the scheme likely loses first-order accuracy. A numerical scan of the linear-reproduction identity at nearby offsets would quantify how precise the shift must be.
The construction suggests a general recipe: take any compact base kernel and add a trigonometric correction whose phase cancels on two staggered grids; higher harmonic terms of the same family could raise continuity order beyond $C^2$ without enlarging the stencil.
Because the momentum-conservation argument only uses that transfers are weighted averages over the two grids, other affine-carrying transfer schemes such as polynomial Particle-In-Cell could likely be ported to this dual-grid framework; the authors mention PolyPIC as a future direction but do not develop it.
The doubled grid memory is the main practical cost; a natural extension would decouple the two grid transfers and process them sequentially or on different devices to cut peak memory, a direction the paper only sketches in its limitations.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's the short version. The paper proposes a genuinely new compact kernel, K1(x)=1-|x|+(1/2π)sin(2π|x|), and shows that when you use it on two staggered grids offset by ±Δx/4 you get partition of unity and linear precision with only 16 nodes per particle in 3D. That dual-grid offset trick is the real contribution, and I haven't seen it in the MPM literature. The paper is also honest about the cost: doubled grid memory and some extra complexity in the MLS momentum matrix.

The kernel construction itself is clean. The derivation from a sine basis is somewhat ad hoc but well-motivated. The momentum conservation proofs, once you correct the G2P formula, follow the standard APIC arguments. The implementation effort is real: CUDA and Taichi versions, stress tests at tens of millions of particles, and a direct energy-decay comparison for numerical diffusion. The performance numbers show a modest speedup, which is plausible given the reduced kernel support.

Now the soft spots. The stress-test note is correct: Equation 17 as printed is mass-weighted G2P, not the standard APIC interpolation. With that formula a single free particle would lose momentum each step, which contradicts the reported results. The supplemental proof of linear momentum conservation has an invalid step: it assumes sum_p w_{i,p}=1 for each grid node, which is not true in general. The fix is simple: use v_p^{new} = (1/2) sum_k sum_i w_{i,p,G_k} \tilde{v}_{i,G_k}. With that, momentum conservation follows by swapping sums. The fact that the open-source code and the momentum plots behave well strongly suggests these are typos, not conceptual errors. Still, as printed the paper cannot serve as a reference implementation.

There's also a typo in the deformation gradient update, Eq. 19, which uses F_{t+1} on both sides, and a garbled line in the supplemental first-order accuracy proof. Both need cleaning.

The fracture behavior discussion is acceptable but slightly oversold: the paper frames easier fracture as a feature, then admits it can be unwanted and needs higher particle counts. That's an honest limitation, not a flaw.

Bottom line: this deserves a serious referee. The core idea is new and likely correct, the experiments are substantive, and the errors are fixable. I would not cite it as a reference until the authors correct the equations, but I'd want to see the revised version. If you're choosing papers for a reading group, it's a good case study in how a strong method can be obscured by presentation errors.

Referee Report

4 major / 6 minor

Summary. The paper introduces CK-MPM, a material point method based on a C^2-continuous compact kernel K1(x)=1-|x|+(1/2π)sin(2π|x|) supported on |x|≤1. The kernel is used on two staggered grids offset by ±1/4 Δx, giving 16 grid nodes per particle in 3D (double the linear kernel's 8 nodes). The authors prove partition of unity and linear reproduction for the dual-grid setting, integrate the kernel with PIC, APIC, and MLS-MPM, and claim linear and angular momentum conservation, reduced numerical diffusion, and faster G2P2G than quadratic B-spline MPM. The claims are supported by unit tests, comparisons, large-scale stress tests, and an open-source implementation.

Significance. If the formulation is corrected, the kernel offers a practically attractive trade-off: C^2 continuity with only 16 nodes per particle, addressing the cell-crossing instability at lower cost than the 27-node quadratic B-spline. The dual-grid linear-reproduction construction is a neat, explicit idea, and the paper ships open-source code plus quantitative momentum-conservation tests at the 1e-5 level, which support the intended implementation. The main value is in demonstrating that a smooth, compact, two-grid transfer can match or beat quadratic B-spline MPM on performance and diffusion. However, the written equations contain errors in the central G2P update and the deformation-gradient update, so the paper cannot currently serve as a reliable reference until those are fixed.

major comments (4)

[§4.3.4, Eq. (17)] The printed grid-to-particle update v_p^{new} = (1/(2 m_p)) Σ_{k∈{±1}} Σ_i w_{i,p,G_k} m_{i,G_k} \tilde v_{i,G_k} does not conserve linear momentum, even in a force-free single-particle test: substituting m_{i,G_k} = w_{i,p,G_k} m_p gives v_p^{new} = v_p (1/2) Σ_k Σ_i w_{i,p,G_k}^2, which is strictly less than v_p because each grid's weights are nonnegative and sum to one. The standard unweighted interpolation v_p^{new} = (1/2) Σ_{k,i} w_{i,p,G_k} \tilde v_{i,G_k}, together with m_{i,G_k} = Σ_p w_{i,p,G_k} m_p, conserves momentum by swapping the order of summation; the reported 1.06e-5 momentum error strongly suggests that this unweighted form is what the implementation computes. The main text must be corrected to match the conservation proof and the code.
[Supplemental §2, proof of Theorem 2.1] The proof of linear momentum conservation contains the step Σ_i m_i \tilde v_i = Σ_i m_i \tilde v_i (Σ_p w_{i,p}), which assumes Σ_p w_{i,p} = 1 for every grid node. The correct identity is m_i = Σ_p w_{i,p} m_p, and Σ_p w_{i,p} is not generally 1 for a finite particle set. With the corrected unweighted G2P formula, the conservation proof is valid after exchanging summation order; as printed, the proof is invalid and must be rewritten together with Eq. (17).
[§4.3.5, Eq. (19)] The deformation gradient update writes (F_{p,G0,t_{n+1}})^α_β = (δ^α_ν + Δt ∂v^α/∂x^ν) (F_{p,G0,t_{n+1}})^ν_β, so the unknown new state appears on the right-hand side. The right-hand side should be (F_{p,G0,t_n})^ν_β, as in the correctly stated pipeline equation in §3.2. This typo would mislead an implementer and must be fixed.
[§4.1 and §4.2] The kernel K1(x) defined in Eq. (4) has support |x| ≤ 1, so a particle is associated with 8 nodes on each of the two grids, or 16 nodes in total; the text nevertheless states a 'kernel radius of 2' in §4.1 and repeats 'since the kernel has a radius of 2, there are eight grid nodes in total' in §4.2. This terminology is internally inconsistent with the derivation and with the stated doubling of the linear kernel's 8 nodes, and it should be corrected to something like 'support width of 2 (radius 1)'.

minor comments (6)

[§4.2, Eq. (10)] The notation 'xG0' in the kernel argument is undefined; it should be 'x_{p,G0}' (or 'x_{G0}') for consistency with the particle position x_p used in Eq. (6).
[Supplemental §1] The proof of Eq. (1) contains corrupted display artifacts (e.g., '1/√︁√︂oductdi√︄√︁display') that make part of the derivation unreadable; the PDF should be regenerated so the proof is fully legible.
[§5.1] The exact ±1/4 Δx offset is load-bearing for the first-order accuracy proof in Supplemental §1; please add an explicit statement that this offset must be preserved exactly in the dual-grid block layout and in the fused G2P2G kernel.
[§6.2.2] The heading 'Fracture A voidance' contains a typo and should read 'Fracture Avoidance'.
[§6.1] The angular momentum test reports an L∞ error rate of 6e-3, which is about three orders of magnitude larger than the linear momentum error of 1e-5; a brief explanation of why this residual is acceptable (e.g., time-integration or affine-correction effects) would strengthen the conservation claim.
[§4.5 and Supplemental §4] The MLS derivation uses the same symbol K with different argument order (K(x_G0 - x_i,G_k) vs. K(x_i,G_k - x_G0)); this is harmless since the kernel is even, but the notation should be unified for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity identified: the kernel and dual-grid offset are constructed from explicit requirements, and the momentum conservation proofs are algebraic, not fitted to or derived from the paper's own measurements.

full rationale

The paper's derivation chain is self-contained and construction-based, not an input–output cycle. The compact kernel K1(x) = 1 - |x| + (1/(2π))sin(2π|x|) is derived in Section 4.1 from explicitly stated requirements: normalization, monotonicity, non-negativity, compactness, Dirac-delta convergence, C^2-continuity, and partition of unity. The partition identity K1(x)+K1(1-x)=1 (Eq. 8) holds by construction of the chosen sinusoid, and it is used to prove the constant-reproduction property (Eq. 6). The linear-reproduction property (Eq. 7) is then achieved by placing the kernel on two staggered grids offset by ±Δx/4; the supplement shows that the sine terms cancel exactly for this offset, giving Eq. 10. This is a mathematical construction aimed at satisfying stated design criteria, not a parameter fitted to the experiment results reported later. The PIC, APIC, and MLS conservation arguments in the supplement follow the standard algebraic structure of MPM/APIC proofs and do not import a self-citation as the load-bearing premise. The paper cites Wang et al. 2020 (which includes two of the present authors) as the GPU implementation framework and as a performance baseline, but that citation is used as an independently published, open-source reference system for benchmarking; it is not invoked to justify the kernel's correctness or to forbid alternative kernels. The skeptical concern about Eq. 17, where the mass-weighted grid-to-particle interpolation would not conserve momentum for a single free particle, is a potential typographical or algorithmic error in the written update; even if valid, it is a correctness flaw, not circularity, since the theorem does not assume the conclusion. No quoted step reduces a prediction to its own fitted input, and no uniqueness theorem is imported from the authors' own prior work. Accordingly, the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 2 invented entities

The method introduces one hand-chosen construction offset and one mode-truncation choice for the kernel; both are design decisions, not fits to experimental data. The axioms are standard continuum/MPM assumptions plus the standard isotropic singular-value property used in the angular momentum proof. The invented entities are the kernel function and the dual grid, both with public falsifiable handles through the open-source code and the conservation tests.

free parameters (2)

Dual-grid offset = ±1/4 Δx
Chosen by hand so that the sine terms cancel in the proof of linear reproduction (Eq. 10). Any other offset breaks the cancellation and the first-order accuracy property.
Kernel mode truncation = 1/(2π) coefficient for n=2 only
The paper keeps only the n=2 Fourier mode of the smoothing function for computational efficiency. The coefficient is then fixed by the derivative condition, but the truncation itself is a design simplification.

assumptions (4)

standard math The kernel K1(x) = 1 - |x| + (1/(2π)) sin(2π|x|) satisfies partition of unity K1(x) + K1(1-x) = 1 and normalization ∫K1 dx = 1.
Used in Sec. 4.2 and the supplemental to prove Eq. (6) and Eq. (10).
domain assumption The weak form of continuum mechanics and the MPM discretization follow the standard formulation of Jiang et al. 2016.
Sec. 3.1 adopts this formulation without re-deriving it.
domain assumption Isotropic hyperelastic materials have F and P sharing the same singular vectors, so P = U Σ̂ V^T when F = UΣV^T.
Supplemental Sec. 3, Eq. (7)-(8), used in the angular momentum conservation proof for APIC.
standard math The MLS least-squares approximation with polynomial basis is valid and the momentum matrix M is invertible.
Sec. 4.5 and Supplemental Sec. 4 rely on the EFG/MLS formulation.

invented entities (2)

Dual-grid system (G-, G+) with ±1/4 Δx offset independent evidence
purpose: Restores first-order linear reproduction (Eq. 10) for a compact kernel that is supported on only one cell.
Its effect is observable through the momentum conservation unit tests and the open-source implementation; third parties can verify without this paper.
Compact C^2 kernel K1(x) = 1 - |x| + (1/(2π)) sin(2π|x|) independent evidence
purpose: Provides C2-continuous particle-grid transfer with single-cell support.
The kernel is defined in closed form and its properties are verified by direct calculation and in the released code; not a hidden entity.

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Cite this review

Pith. "Pith review of CK-MPM: A Compact-Kernel Material Point Method." pith.science (2026). https://pith.science/paper/5EWGQZVL

@misc{pith2026241210399,
  author       = {Pith},
  title        = {Pith review of: CK-MPM: A Compact-Kernel Material Point Method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5EWGQZVL}},
  note         = {Machine review of arXiv:2412.10399}
}

read the original abstract

The Material Point Method (MPM) has become a cornerstone of physics-based simulation, widely used in geomechanics and computer graphics for modeling phenomena such as granular flows, viscoelasticity, fracture mechanics, etc. Despite its versatility, the original MPM suffers from cell-crossing instabilities caused by discontinuities in particle-grid transfer kernels. Existing solutions mostly mitigate these issues by adopting smoother shape functions, but at the cost of increased numerical diffusion and computational overhead due to larger kernel support. In this paper, we propose a novel C^2-continuous compact kernel for MPM that achieves a unique balance in terms of stability, accuracy, and computational efficiency. Our method integrates seamlessly with Affine Particle-In-Cell (APIC) and Moving Least Squares (MLS) MPM, while only doubling the number of grid nodes associated with each particle compared to linear kernels. At its core is an innovative dual-grid framework, which associates particles with grid nodes exclusively within the cells they occupy on two staggered grids, ensuring consistent and stable force computations. We demonstrate that our method can be conveniently implemented using a domain-specific language, Taichi, or based on open-source GPU MPM frameworks, achieving faster runtime and less numerical diffusion compared to quadratic B-spline MPM. Comprehensive validation through unit tests, comparative studies, and stress tests demonstrates the efficacy of our approach in conserving both linear and angular momentum, handling stiff materials, and scaling efficiently for large-scale simulations. Our results highlight the transformative potential of compact, high-order kernels in advancing MPM's capabilities for stable, accurate, and high-performance simulations.

Figures

Figures reproduced from arXiv: 2412.10399 by the authors.

**Figure 1.** Large-scale simulations of a sandcastle (left) and a fire hydrant (right) destroyed by high-speed balls, both performed using our compact-kernel [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** Plot of linear (blue), quadratic B-spline (red), and our compact (yel [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Comparison of interpolation patterns of different kernels in 2D. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (18 more)

**Figure 4.** Figure 4: Linear Momentum Conservation. Plot of the conserved 𝑥−component total linear momentum (blue) and the linear momentum of two spheres colliding (green and orange). 5.2 Taichi Implementation In addition to the CUDA implementation, we also provide a Taichibased implementa…

**Figure 5.** Figure 5: Angular Momentum Conservation. Evolution of x-,y-,zcomponent of the total angular momentum of a rotating bar simulation; all components are accurately preserved over time. sphere is approximately 2905.69 kg · m/s, while the total initial linear momentum of the system…

**Figure 6.** Figure 6: Jelly Falling. each example, confirming that G2P2G remains the dominant cost across all configurations. We also compare the memory footprints of MPM implementations using quadratic kernels (as in [Wang et al. 2020]) and our compact kernel approach. Particle representat…

**Figure 8.** Figure 8: Oreo Drop. The initial drop height of the Oreo is set to 16 256m, and the simulation is conducted with gravity 𝑔 = −9.8 m/s2 . As shown in [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 11.** Figure 11: Contact Behavior Test. Both the ball and the cylinder are simulated using the Fixed Corotated hyperelasticity model with Young’s modulus 𝐸 = 106𝑃𝑎 and 𝜈 = 0.4. We initialize the grid Δ𝑥 = 1 256𝑚, and the hollow cylinder have inner diameter of 8 256𝑚. We simulate case…

**Figure 10.** Figure 10: Twisting Elastic Bar. The yellow bar is simulated with quadratic kernel with 8 particles per cell. Others are simulated using compact kernel with 8 (purple), 16 (green), and 27 (blue) particles per cell. To examine the performance of our method when simulating elastic…

**Figure 9.** Figure 9: Sand Armadillos. We attribute this improved energy preservation to the compact kernel’s ability to better capture high-frequency features with minimal smoothing. 6.3 Stress tests To evaluate the stability and robustness of our compact-kernel MPM under extreme conditio…

**Figure 12.** Figure 12: Numerical Diffusion. Kinetic, elastic, and total energy plotted on a logarithmic scale for simulations using the compact and quadratic kernels [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]

**Figure 13.** Figure 13: Fluid Flush with Two Loongs. The grid has resolution of (512, 768, 512) and grid spacing of 1 512𝑚. As illustrated in [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]

**Figure 14.** Figure 14: Fire Hydrant Pumping. (a) Before / During Impact (b) After Impact [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]

**Figure 15.** Figure 15: Bullet Impact on Tungsten [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]

**Figure 16.** Figure 16: Bullet Impact on Tungsten. Cross-sectional view of stress distribution. presents challenges for scenarios requiring fracture-free large deformations. In such cases, increasing the particle sampling density per cell could mitigate unwanted fractures. Finally, we envi…

**Figure 1.** Figure 1: Two Dragons Falling. Compact Kernel [PITH_FULL_IMAGE:figures/full_fig_p023_1.png]

**Figure 2.** Figure 2: Two Dragons Falling. Quadratic Kernel [PITH_FULL_IMAGE:figures/full_fig_p023_2.png]

**Figure 3.** Figure 3: Sand Armadillo. Compact Kernel [PITH_FULL_IMAGE:figures/full_fig_p024_3.png]

**Figure 4.** Figure 4: Sand Armadillo. Quadratic Kernel [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]

**Figure 5.** Figure 5: Dam Break. Compact Kernel [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]

**Figure 6.** Figure 6: Dam Break. Quadratic Kernel [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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[4] [2013]

ACM Transactions on Graphics (TOG) 32, 4 (2013), 1–10

A material point method for snow simulation. ACM Transactions on Graphics (TOG) 32, 4 (2013), 1–10. Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle. 2014. Augmented MPM for phase-change and varied materials. ACM Transactions on Graphics (TOG) 33, 4 (2014), 1–11. Haozhe Su, Tao Xue, Chengguizi Han, Chenfanf...

work page 2013

[5] [2015]

ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–10

The affine particle-in-cell method. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–10. Chenfanfu Jiang, Craig Schroeder, and Joseph Teran. 2017b. An angular momentum conserving affine-particle-in-cell method. J. Comput. Phys. 338 (2017), 137–164. Chenfanfu Jiang, Craig Schroeder, Joseph Teran, Alexey Stomakhin, and Andrew Selle

work page 2015

[6] [2016]

A Thermomechanical Hybrid Incompressible Material Point Method

The material point method for simulating continuum materials. In Acm siggraph 2016 courses. 1–52. Victoria Kala, Jingyu Chen, David Hyde, Alexey Stomakhin, and Joseph Teran. 2024. A Thermomechanical Hybrid Incompressible Material Point Method. arXiv preprint arXiv:2408.07276 (2024). Gergely Klár, Theodore Gast, Andre Pradhana, Chuyuan Fu, Craig Schroeder,...

work page Pith review arXiv 2024

[7] [2017]

ACM Transactions on Graphics (TOG) 36, 4 (2017), 1–17

A multi-scale model for simulating liquid-hair interactions. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1–17. Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, and Joseph Teran. 2017. A polynomial particle-in-cell method. ACM Transactions on Graphics (TOG) 36, 6 (2017), 1–12. Ming Gao, Andre Pradhana Tampubolon, Chenfanfu Jiang, and Eftychios Sifa...

work page 2017

[8] [2019]

Principles towards Real-Time Simulation of Material Point Method on Modern GPUs

A thermomechanical material point method for baking and cooking. ACM Transactions on Graphics (TOG) 38, 6 (2019), 1–14. Yu Fang, Minchen Li, Ming Gao, and Chenfanfu Jiang. 2019. Silly rubber: an implicit material point method for simulating non-equilibrated viscoelastic and elastoplastic 14 • Michael Liu, Xinlei Wang, and Minchen Li solids. ACM Transactio...

work page Pith review arXiv 2019