[ { "path": "table_paper/2407.00046v1.json", "table_id": "1", "section": "6.4", "all_context": [ "We compare with the original IPC, making sure it utilizes full parallelization on the CPU by compiling CHOLMOD with Intel MKL and run the simulation on an Intel Core i9 13900K processor (24 cores), enabling a 24-thread Cholesky factorization for solving the linear systems.", "Figure 28 illustrates the effectiveness of two different computational methods in simulating the twisting of a cylindrical mat.", "Both methods produce visually comparable results; however, our method significantly outperforms IPC in computational efficiency, processing steps 19.3 faster on average.", "The demonstrated efficiency indicates that our method could provide considerable benefits to industries requiring fast and accurate simulations.", "Table 1 showcases the statistics and quantifies the speedup achieved in representative cases relative to IPC.", "In the study by Lan et al.", "(2023 ), a novel GPU-accelerated algorithm is introduced for FEM elastodynamic simulations, leveraging interior-point methods to effectively handle complex scenarios involving extensive contact and collisions.", "This algorithm is notable for its use of complementary coloring and a hybrid sweep approach, which are well-suited for such applications.", "Nonetheless, these strategies may not fully address the specific challenges posed by stiff problems, such as significantly large stress resulting from challenging boundary conditions as in the simulation of twisting rods (Figure 4 ).", "This example underscores our method s capability by stress testing four stiff rods with a Young s modulus of 10 MPa.", "These rods are subject to high-speed torsion from both ends, achieving an angular velocity of 5/12 revolutions per second over 18 complete turns.", "The image captures the deformation pattern, reflecting the rods structural integrity and the material s resistance to the applied forces.", "Our method demonstrates proficiency in handling such demanding tests with large time steps, ensuring accurate results and computational efficiency.", "The concurrent development of another GPU-based IPC method, termed GIPC, employs a Gauss-Newton approximation for the contact Hessian matrix.", "This method solves the IPC system without the need for numerical eigendecompositions, an operation that is not easy to parallelize on the GPU.", "In contrast, our approach focuses on reformulating the nonlinear problem to make it easier to solve for both Newton s method and CG solvers.", "In the comparative tests (see Figure 29 ), we used simulations of stacked armadillos and octopuses with frictional contacts (where ) and aligned the Newton tolerance for both methods.", "Our method consistently outperforms GIPC, achieving up to in speedup and in Newton convergence.", "Specifically, GIPC encounters challenges in large-scale simulations due to suboptimal convergence speeds.", "While GIPC uses Newton-PCG for optimization, its performance can still be significantly affected by the conditioning of the system.", "The Multilevel Additive Schwarz (MAS) preconditioner utilized in GIPC effectively smooths out low-frequency errors commonly found in hyperelastic materials but struggles with the high-frequency errors that are typical in scenarios involving frictional contacts, leading to difficulties in larger-scale frictional contact simulations.", "" ], "target_context_ids": [ 4 ], "selected_paragraphs": [ "[paragraph id = 4] Table 1 showcases the statistics and quantifies the speedup achieved in representative cases relative to IPC." ], "table_html": "
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Table 1. Statistics for Testing Scenarios. This table details the total numbers of tetrahedra (#tets), Degrees of Freedom (#DOFs), and surface triangles (#tris). Key simulation parameters such as time step (), material density, Young’s Modulus (), Poisson Ratio (), collision offset (), and frictional coefficient () are provided. Additionally, the table includes both average and maximum numbers of constraints (#cons), the total number of Newton iterations per step, the average computational cost per step, and the comparative speedup achieved against IPC. Note that we simply use the same value for the friction mollification threshold and .
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Scenario#tets / #DOFs / #tris\n (s)\n\n\n\n\n\n\n\n\n
\ndensity (kg/m3),\n
\n (Pa), \n
\n		\n, \n\n\n\n\n\n\n\n\n
#cons
\n(avg. / )\n
\n		\n\n\n\n\n\n\n\n
avg. #iters
(Newton)
\n		\n\n\n\n\n\n\n\n
avg. cost
per-step (s)
\n		\n\n\n\n\n\n\n\n
speedup
vs. IPC
\n
Puffer Balls on Nets1.76M / 801K / 1.6M1/301e3, 5e5 / 1e9, 0.41e-30.3228K / 292K156.8427
Dragons-Pachinko1.49M / 379K / 773K1/30\n1e3, \n\n\n\n\n\n\n\n
\n5e5 ()/\n
\n1e6 ()\n
\n, 0.4\n		1e-30.34.9K / 18K41.429.1
Staircase-Armadillos300K / 94K / 187K1/301e3, 7.5e5, 0.41e-30.53.2K / 3.2K3826.7
Staircase-Dragons376K / 120K / 240K1/301e3, 7.5e5, 0.41e-30.53K / 5.4K41.928.5
Roller Test100K / 31K / 62K1/301e3, 1e6, 0.41e-30.91.6K / 5.8K35.412.5
Armadillos & Bowl826K / 192K / 238K1/301e3, 5e5, 0.41e-30.12.2K / 9.7K8.23.4
\n\n\n\n\n\n\n\n
Crabs on Nets
(light crabs)
\n		2.2M / 810K / 1.2M1/301e2 / 1e3, 5e5, 0.41e-30.332K / 52K34.548.8
Twisting Rods355K / 70.4K / 51.6K1/301e3, 1e7, 0.41e-30617K / 5.7M24.115.54
\n\n\n\n\n\n\n\n
Twisting
Cylindrical Mat
\n		64K / 20.9K / 41.8K1/301e3, 1e7, 0.41e-3060K / 147K18.85.7
Noodles-200934K / 375K / 749K1/301e3, 5e5, 0.41e-30.348.9K / 146.3K39.749.5
Noodles-3001.4M / 562K / 1.1M1/301e3, 5e5, 0.41e-30.3132.1K / 276K60.9109.6
\nT-rex \n9M / 2.2M / 2.9M1/301e3, 5e5, 0.41e-30.3100.5K / 308.4K25.6183.4N/A
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", "perturb_sentence_id": [ 4, 5 ], "output": { "perturbed_statement": "[paragraph id = 4] Table 1 showcases the statistics and quantifies the speedup achieved in irrelevant cases relative to IPC. In the study by Lan et al.", "perturbed_explanation": "1. The original explanation states that Table 1 presents statistics and quantifies speedup in representative cases.\n2. The statement incorrectly mentions 'irrelevant cases' rather than 'representative cases'. This error changes the focus and suggests that the data is not relevant to the core focus of the study, thereby misrepresenting the study's findings." } } ]