AutoMat: automatic differentiation for generalized standard materials on GPUs

[1]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[2]  I. Cormeau,et al.  Numerical stability in quasi‐static elasto/visco‐plasticity , 1975 .

[3]  L. Dormieux,et al.  Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites , 2012 .

[4]  Jean Utke,et al.  OpenAD/F: A Modular Open-Source Tool for Automatic Differentiation of Fortran Codes , 2008, TOMS.

[5]  M. Diehl,et al.  A spectral method solution to crystal elasto-viscoplasticity at finite strains , 2013 .

[6]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[7]  Andrea Walther,et al.  Differentiating Fixed Point Iterations with ADOL-C: Gradient Calculation for Fluid Dynamics , 2006, HPSC.

[8]  C. Farhat International Journal for Numerical Methods in Engineering , 2019 .

[9]  M. Schneider Convergence of FFT‐based homogenization for strongly heterogeneous media , 2015 .

[10]  Hervé Moulinec,et al.  A computational scheme for linear and non‐linear composites with arbitrary phase contrast , 2001 .

[11]  M. Schneider,et al.  On Quasi‐Newton methods in fast Fourier transform‐based micromechanics , 2019, International Journal for Numerical Methods in Engineering.

[12]  L. Shampine,et al.  A 3(2) pair of Runge - Kutta formulas , 1989 .

[13]  Andrea Walther,et al.  Automatic differentiation of explicit Runge-Kutta methods for optimal control , 2007, Comput. Optim. Appl..

[14]  Martin Diehl,et al.  Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials , 2013 .

[15]  W. Marsden I and J , 2012 .

[16]  Felix Fritzen,et al.  Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems , 2018 .

[17]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[18]  Thomas Böhlke,et al.  Reduced basis homogenization of viscoelastic composites , 2013 .

[19]  Takahiro Katagiri,et al.  Implementation and Evaluation of 3D Finite Element Method Application for CUDA , 2012, VECPAR.

[20]  V. K. Arya,et al.  On the numerical integration of viscoplastic models , 1986 .

[21]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[22]  W. Voigt,et al.  Lehrbuch der Kristallphysik , 1966 .

[23]  Roger P. Pawlowski,et al.  Efficient Expression Templates for Operator Overloading-based Automatic Differentiation , 2012, ArXiv.

[24]  Hervé Moulinec,et al.  A numerical method for computing the overall response of nonlinear composites with complex microstructure , 1998, ArXiv.

[25]  Quoc Son Nguyen,et al.  Sur les matériaux standard généralisés , 1975 .

[26]  Pierre Suquet,et al.  A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations , 2016 .

[27]  Luc Dormieux,et al.  FFT-based methods for the mechanics of composites: A general variational framework , 2010 .

[28]  Peter Eberhard,et al.  Automatic differentiation of numerical integration algorithms , 1999, Math. Comput..

[29]  Andrea Walther,et al.  Automatic Differentiation of an Entire Design Chain for Aerodynamic Shape Optimization , 2007 .

[30]  Mohamed Rouainia,et al.  Explicit Runge–Kutta methods for the integration of rate-type constitutive equations , 2008 .

[31]  Robin J. Hogan,et al.  Fast Reverse-Mode Automatic Differentiation using Expression Templates in C++ , 2014, ACM Trans. Math. Softw..

[32]  M. Schneider,et al.  Efficient fixed point and Newton–Krylov solvers for FFT-based homogenization of elasticity at large deformations , 2014 .

[33]  F. Krogh,et al.  Solving Ordinary Differential Equations , 2019, Programming for Computations - Python.

[34]  H. Moulinec,et al.  A fast numerical method for computing the linear and nonlinear mechanical properties of composites , 1994 .

[35]  Krzysztof Banas,et al.  3D finite element numerical integration on GPUs , 2010, ICCS.

[36]  L. Gélébart,et al.  Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials , 2013 .

[37]  Didier Auroux,et al.  Optimal parameters identification and sensitivity study for abrasive waterjet milling model , 2016, 1605.08583.

[38]  Ralph Müller,et al.  A scalable multi‐level preconditioner for matrix‐free µ‐finite element analysis of human bone structures , 2008 .

[39]  Sachin S. Gautam,et al.  GPU-warp based finite element matrices generation and assembly using coloring method , 2019, J. Comput. Des. Eng..

[40]  P. Alam ‘G’ , 2021, Composites Engineering: An A–Z Guide.

[41]  Andrea Walther,et al.  Getting Started with ADOL-C , 2009, Combinatorial Scientific Computing.

[42]  M. Schneider,et al.  Mixed boundary conditions for FFT-based homogenization at finite strains , 2016 .

[43]  Lars Ruthotto,et al.  Layer-Parallel Training of Deep Residual Neural Networks , 2018, SIAM J. Math. Data Sci..

[44]  Ralph Müller,et al.  A scalable multi‐level preconditioner for matrix‐free µ‐finite element analysis of human bone structures , 2008 .

[45]  Adrian Sandu,et al.  Forward and adjoint sensitivity analysis with continuous explicit Runge-Kutta schemes , 2009, Appl. Math. Comput..

[46]  P. Y. Wu Products of positive semidefinite matrices , 1988 .

[47]  Mathias Wilke,et al.  Gewöhnliche Differentialgleichungen und dynamische Systeme , 2011 .

[48]  Adrian Sandu,et al.  Forward, Tangent Linear, and Adjoint Runge-Kutta Methods in KPP-2.2 , 2006, International Conference on Computational Science.

[49]  F. Willot,et al.  Fourier-based schemes for computing the mechanical response of composites with accurate local fields , 2014, 1412.8398.

[50]  U. Naumann,et al.  Meta Adjoint Programming in C + + , 2017 .

[51]  M. Schneider,et al.  The composite voxel technique for inelastic problems , 2017 .

[52]  Nicolas R. Gauger,et al.  High-Performance Derivative Computations using CoDiPack , 2017, ACM Trans. Math. Softw..

[53]  M. Schneider A dynamical view of nonlinear conjugate gradient methods with applications to FFT-based computational micromechanics , 2020, Computational Mechanics.

[54]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[55]  C. Sauder,et al.  Analysis of the damage initiation in a SiC/SiC composite tube from a direct comparison between large-scale numerical simulation and synchrotron X-ray micro-computed tomography , 2019, International Journal of Solids and Structures.

[56]  M. Schneider,et al.  FFT‐based homogenization for microstructures discretized by linear hexahedral elements , 2017 .

[57]  Adrian Sandu,et al.  On the discrete adjoints of adaptive time stepping algorithms , 2009, J. Comput. Appl. Math..

[58]  Cyril Flaig,et al.  Bone structure analysis on multiple GPGPUs , 2014, J. Parallel Distributed Comput..

[59]  R. Ma,et al.  FFT-based homogenization of hypoelastic plasticity at finite strains , 2019, Computer Methods in Applied Mechanics and Engineering.

[60]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[61]  Nicolas R. Gauger,et al.  Expression templates for primal value taping in the reverse mode of algorithmic differentiation , 2018, Optim. Methods Softw..

[62]  Jan Novák,et al.  Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients , 2010, J. Comput. Phys..

[63]  Adrian Sandu,et al.  On the Properties of Runge-Kutta Discrete Adjoints , 2006, International Conference on Computational Science.

[64]  S. Hartmann,et al.  Automatic differentiation for stress and consistent tangent computation , 2014, Archive of Applied Mechanics.

[65]  M. Schneider On the Barzilai‐Borwein basic scheme in FFT‐based computational homogenization , 2019, International Journal for Numerical Methods in Engineering.

[66]  Javier Segurado,et al.  On the accuracy of spectral solvers for micromechanics based fatigue modeling , 2018, Computational Mechanics.

[67]  M. Kabel,et al.  Runtime optimization of a memory efficient CG solver for FFT-based homogenization: implementation details and scaling results for linear elasticity , 2019, Computational Mechanics.

[68]  Yang Chen,et al.  A FFT solver for variational phase-field modeling of brittle fracture , 2019, Computer Methods in Applied Mechanics and Engineering.

[69]  M. Schneider,et al.  Computational homogenization of elasticity on a staggered grid , 2016 .

[70]  Adrian Sandu,et al.  Reverse Automatic Differentiation of Linear Multistep Methods , 2008 .