Related papers: A Flexible, Parallel, Adaptive Geometric Multigrid…
Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
We present multigrid methods for solving elliptic partial differential equations on arbitrary domains using the nodal ghost finite element method, an unfitted boundary approach where the domain is implicitly defined by a level-set function.…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
It is found that the wave functions of the Gross-Pitaevskii equation (GPE) often vary significantly in different spatial regions, with some components exhibiting sharp variations while others remain smooth. Solving the GPE on a single mesh,…
This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…
This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
General Matrix Multiplication (GEMM) is a critical operation underpinning a wide range of applications in high-performance computing (HPC) and artificial intelligence (AI). The emergence of hardware optimized for low-precision arithmetic…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as…
We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to…
Large-scale parallel numerical simulations are essential for a wide range of engineering problems that involve complex, coupled physical processes interacting across a broad range of spatial and temporal scales. The data structures involved…
Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement…
Graph partitioning, a well studied problem of parallel computing has many applications in diversified fields such as distributed computing, social network analysis, data mining and many other domains. In this paper, we introduce FGPGA, an…