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Finite Element Integration on GPUs

Matthew G. Knepley, Andy R. Terrel
2013 ACM Transactions on Mathematical Software  
We present a novel finite element integration method for low order elements on GPUs.  ...  We achieve more than 100GF for element integration on first order discretizations of both the Laplacian and Elasticity operators.  ...  majority of finite element codes.  ... 
doi:10.1145/2427023.2427027 fatcat:pgpexn6k3bhcbgbfh6uzo6hyme

3D finite element numerical integration on GPUs

Paweł Macioł, Przemysław Płaszewski, Krzysztof Banaś
2010 Procedia Computer Science  
The algorithmic and computational aspects of 3D finite element numerical integration on GPUs are investigated in the paper.  ...  The close interplay between the available computational resources of GPUs and the possible implementation strategies and obtained results is observed.  ...  It also depends on the order of approximation and usually (with some departures for special kinds of problems) is chosen so as to integrate exactly finite element integrals in a reference element.  ... 
doi:10.1016/j.procs.2010.04.121 fatcat:6676ihbzyngolj6d2u3mbbzkt4

Finite Element Integration with Quadrature on the GPU [article]

Matthew G. Knepley and Karl Rupp and Andy R. Terrel
2016 arXiv   pre-print
We present a novel, quadrature-based finite element integration method for low-order elements on GPUs, using a pattern we call thread transposition to avoid reductions while vectorizing aggressively.  ...  On the NVIDIA GTX580, which has a nominal single precision peak flop rate of 1.5 TF/s and a memory bandwidth of 192 GB/s, we achieve close to 300 GF/s for element integration on first-order discretization  ...  Providing a general, low-order integration method for the GPU based on quadrature will be necessary for the wider use of these architectures by finite element codes.  ... 
arXiv:1607.04245v1 fatcat:z7shx7tygradpesq7lvkniht4q

Numerical integration on GPUs for higher order finite elements

Krzysztof Banaś, Przemysław Płaszewski, Paweł Macioł
2014 Computers and Mathematics with Applications  
The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations.  ...  The design of suitable GPU kernels is investigated in the context of general purpose integration procedures, as well as particular example applications.  ...  Thorough investigations of the finite element assembly process on GPUs were presented in [25] .  ... 
doi:10.1016/j.camwa.2014.01.021 fatcat:hxdvmj2tpndydgr22bhgjqrbie

FINITE ELEMENT MATRIX GENERATION ON A GPU

Adam Dziekonski, Piotr Sypek, Adam Lamecki, Michal Mrozowski
2012 Electromagnetic Waves  
This paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements.  ...  The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly.  ...  A Tesla C2075 GPU donation from Nvidia is also gratefully acknowledged.  ... 
doi:10.2528/pier12040301 fatcat:4ivretp5f5a6xavcvejngldibi

GPU Accelerated Finite Element Assembly with Runtime Compilation [article]

Tao Cui, Xiaohu Guo, Hui Liu
2018 arXiv   pre-print
There are many researches focus on finite element method with GPUs. However, most of the works are specific to certain problems and applications.  ...  In this paper, we present architecture and implementation of finite element assembly for partial differential equations (PDEs) based on symbolic computation and runtime compilation technique on GPU.  ...  In the z direction, a finite element is processed. Fig. 2 A 3D thread block for finite element assembly: (A) A single thread which evaluates the integrand on an single integration point.  ... 
arXiv:1802.03433v1 fatcat:mcyobrwdmbaidckeouwlqbmjwe

A modular framework for deformation and fracture using GPU shaders

Derek John Morris, Eike Falk Anderson, Christopher Peters
2012 2012 18th International Conference on Virtual Systems and Multimedia  
the simulation within shader programs on recent GPU's.  ...  Advances in the graphical realism of modern video games have been achieved mainly through the development of the GPU (Graphics Processing Unit), providing a dedicated graphics co-processor and framebuffer  ...  novel method of connectivity of finite elements used to simulate material fracture on a GPU stream processing architecture.  ... 
doi:10.1109/vsmm.2012.6365934 dblp:conf/vsmm/MorrisAP12 fatcat:qn7i2zqasfdahh4w7t7mjotmn4

Global finite element matrix construction based on a CPU-GPU implementation [article]

Francisco Javier Ramírez-Gil, Marcos de Sales Guerra Tsuzuki and Wilfredo Montealegre-Rubio
2015 arXiv   pre-print
This methodology allows generating the global sparse matrix from any unstructured finite element mesh size on GPUs with little memory capacity, only limited by the CPU memory.  ...  The generation of the global finite element matrix is performed in two steps, computing the local matrices by numerical integration and assembling them into a global system, which has traditionally been  ...  discretization with finite elements (FEs); (ii) Numerical integration of all FEs.  ... 
arXiv:1501.04784v1 fatcat:35c5al4xwjfybmbxv6jziargmi

A GPU-Based Parallel Procedure for Nonlinear Analysis of Complex Structures Using a Coupled FEM/DEM Approach

Lixiang Wang, Shihai Li, Guoxin Zhang, Zhaosong Ma, Lei Zhang
2013 Mathematical Problems in Engineering  
This study reports the GPU parallelization of complex three-dimensional software for nonlinear analysis of concrete structures. It focuses on coupled thermomechanical analysis of complex structures.  ...  The results show that dramatic performance improvements are gained from GPU parallelization.  ...  Finally, conclusions regarding the GPU parallelization are drawn. Coupled Finite/Discrete Element Model Geometric Representation. Li et al.  ... 
doi:10.1155/2013/618980 fatcat:k7wbtb7mwbgt3gm4o4kxejpllq

Finite element numerical integration for first order approximations on multi- and many-core architectures

Krzysztof Banaś, Filip Krużel, Jan Bielański
2016 Computer Methods in Applied Mechanics and Engineering  
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in  ...  The general conclusion is that the finite element numerical integration can achieve sufficient performance on different multi- and many-core architectures and should not become a performance bottleneck  ...  one of computational kernels of finite element codes.  ... 
doi:10.1016/j.cma.2016.03.038 fatcat:m2jlmglvybhurjuwx662ftei2q

Comparison of the Structure of Equation Systems and the GPU Multifrontal Solver for Finite Difference, Collocation and Finite Element Method

P. Lipski, M. Woźniak, M. Paszyński
2015 Procedia Computer Science  
The paper considers recently developed isogeometric versions of the collocation and finite element methods, employing B-splines for the computations and ensuring C p−1 continuity on the borders of elements  ...  The article is an in-depth comparison of numerical solvers and corresponding solution processes of the systems of algebraic equations resulting from finite difference, collocation, and finite element approximations  ...  Figure 7 : 7 Comparison of integration and execution times of our GPU solver for one dimensional multifrontal solver with isogeometric basis functions.  ... 
doi:10.1016/j.procs.2015.05.266 fatcat:ve5fopzusnbdtcrpxkqzesfm5e

GPU-Accelerated 3D Mesh Deformation for Optimization Based on the Finite Element Method

A. Lamecki, A. Dziekonski, L. Balewski, G, Fotyga, M. Mrozowski
2017 Radioengineering  
In order to accomplish this in a very short time numerical integration and the solution of the resulting system of equations are performed using a graphics processing unit (GPU).  ...  This paper discusses a strategy for speeding up the mesh deformation process in the design-byoptimization of high-frequency components involving electromagnetic field simulations using the 3D finite element  ...  For relatively small finite element meshes (where all the data fit on a single GPU), the matrix-assembly process can be executed in stages (3) and (4) .  ... 
doi:10.13164/re.2017.0924 fatcat:p7q42h4kivfuvkh2jj53s34oou

Real-time nonlinear finite element computations on GPU – Application to neurosurgical simulation

Grand Roman Joldes, Adam Wittek, Karol Miller
2010 Computer Methods in Applied Mechanics and Engineering  
models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom.  ...  In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase  ...  The finite element algorithm, as implemented on CPU, is presented in Section 3.  ... 
doi:10.1016/j.cma.2010.06.037 pmid:21179562 pmcid:PMC3003932 fatcat:mpfcgke65famnggxgfksjkisra

GPU accelerated spectral finite elements on all-hex meshes

J.-F. Remacle, R. Gandham, T. Warburton
2016 Journal of Computational Physics  
This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes.  ...  Performance tests demonstrate that problems with over 50 million degrees of freedom can be solved in a few seconds on an off-the-shelf GPU.  ...  Knepley et al [15] described algorithms for efficient evaluation of finite element integrals on GPUs.  ... 
doi:10.1016/j.jcp.2016.08.005 fatcat:7hrof3chlrf3to2syccxl6umyq

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time; Application to non-rigid neuroimage registration

Adam Wittek, Grand Joldes, Mathieu Couton, Simon K. Warfield, Karol Miller
2010 Progress in Biophysics and Molecular Biology  
element procedures implemented on a graphics processing unit (GPU).  ...  In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian  ...  Implementation of algorithms for computing soft tissue deformation on Graphics Processing Unit (GPU) Recent examples of implementation of non-linear finite element algorithms for computing soft tissue  ... 
doi:10.1016/j.pbiomolbio.2010.09.001 pmid:20868706 pmcid:PMC3107968 fatcat:ew6ziwlj5bhxrbldqv4rtfccli
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