SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
An algorithm with linear complexity for interactive, physically-based modeling of large proteins
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Solving stiff differential equations with method of patches
Journal of Computational Physics
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
Long-Time-Step Methods for Oscillatory Differential Equations
SIAM Journal on Scientific Computing
An exponential method of numerical integration of ordinary differential equations
Communications of the ACM
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
SIAM Journal on Numerical Analysis
A Fast Finite Element Solution for Cloth Modelling
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Efficient simulation of inextensible cloth
ACM SIGGRAPH 2007 papers
ACM SIGGRAPH 2008 papers
Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications
Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications
Energy Conservation for the Simulation of Deformable Bodies
IEEE Transactions on Visualization and Computer Graphics
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We investigate the application of exponential integrators to stiff elastodynamic problems governed by second-order differential equations. Classical explicit numerical integration schemes have the shortcoming that the stepsizes are limited by the highest frequency that occurs within the solution spectrum of the governing equations, while implicit methods suffer from an inevitable and mostly uncontrollable artificial viscosity that often leads to a nonphysical behavior. In order to overcome these specific detriments, we devise an appropriate class of exponential integrators that solve the stiff part of the governing equations of motion by employing a closed-form solution. As a consequence, we are able to handle up to three orders of magnitude larger time-steps as with conventional implicit integrators and at the same time achieve a tremendous increase in the overall long-term stability due to a strict energy conservation. The advantageous behavior of our approach is demonstrated on a broad spectrum of complex deformable models like fibers, textiles, and solids, including collision response, friction, and damping.