Related papers: A matrix-free approach for finite-strain hyperelas…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
Matrix-free techniques play an increasingly important role in large-scale simulations. Schur complement techniques and massively parallel multigrid solvers for second-order elliptic partial differential equations can significantly benefit…
Multigrid solvers for hierarchical hybrid grids (HHG) have been proposed to promote the efficient utilization of high performance computer architectures. These HHG meshes are constructed by uniformly refining a relatively coarse fully…
Multigrid methods are asymptotically optimal algorithms ideal for large-scale simulations. But, they require making numerous algorithmic choices that significantly influence their efficiency. Unlike recent approaches that learn optimal…
A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
Unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
We consider the numerical treatment of one of the most popular finite strain models of the viscoelastic Maxwell body. This model is based on the multiplicative decomposition of the deformation gradient, combined with Neo-Hookean…
This article presents a $P_0$ finite element method for boundary value problems for linear elasticity equations. The new method makes use of piecewise constant approximating functions on the boundary of each polytopal element, and is…
We present a space-time multigrid method based on tensor-product space-time finite element discretizations. The method is facilitated by the matrix-free capabilities of the {\ttfamily deal.II} library. It addresses both high-order…
Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO2 containment as a climate change mitigation strategy. These simulations involve solving numerous…
Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…
We develop a matrix-free Full Approximation Storage (FAS) multigrid solver based on staggered finite differences and implemented on GPU in MATLAB. To enhance performance, intermediate variables are reused, and an X-shape Multi-Color…
A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential…
Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…