Related papers: A study of vectorization for matrix-free finite el…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
We introduce an algorithmic framework for performing QR factorization with column pivoting (QRCP) on general matrices. The framework enables the design of practical QRCP algorithms through user-controlled choices for the core subroutines.…
Developing efficient hardware accelerators for mathematical kernels used in scientific applications and machine learning has traditionally been a labor-intensive task. These accelerators typically require low-level programming in Verilog or…
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…
Discrete Fracture Network models are largely used for very large scale geological flow simulations. For this reason numerical methods require an investigation of tools for efficient parallel solutions on High Performance Computing systems.…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the…
In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the…
We introduce Fireshape, an open-source and automated shape optimization toolbox for the finite element software Firedrake. Fireshape is based on the moving mesh method and allows users with minimal shape optimization knowledge to tackle…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…
This paper presents the design of HELIX, an end-to-end verified code generation system with a focus on the intersection of high-performance and high-assurance numerical computing. The code generation can be fine-tuned to generate efficient…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed…
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…
The scientific community use PDEs to model a range of problems. The people in this domain are interested in visualizing their results, but existing mechanisms for visualization can not handle the full richness of computations in the domain.…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…
Electrical machines commonly consist of moving and stationary parts. The field simulation of such devices can be very demanding if the underlying numerical scheme is solely based on a domain discretization, such as in case of the Finite…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
Matrix-free finite element implementations for large applications provide an attractive alternative to standard sparse matrix data formats due to the significantly reduced memory consumption. Here, we show that they are also competitive…