相关论文: A fast and robust discrete FFT-based solver for co…

We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast…

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…

We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…

In this paper we establish a stability barrier of a class of high-order Hermite-type discretization of 1D advection equations underlying the hybrid-variable (HV) and active flux (AF) methods. These methods seek numerical approximations to…

Fast and high-order accurate algorithms for three dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a…

Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature…

We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations…

We present a Ritz-Galerkin discretization on sparse grids using pre-wavelets, which allows to solve elliptic differential equations with variable coefficients for dimension $d=2,3$ and higher dimensions $d>3$. The method applies multilinear…

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…

Fast-Fourier Transform (FFT) methods have been widely used in solid mechanics to address complex homogenization problems. However, current FFT-based methods face challenges that limit their applicability to intricate material models or…

We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…

The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic…

We introduce an FFT-based solver for the combinatorial continuous maximum flow discretization applied to computing the minimum cut through heterogeneous microstructures. Recently, computational methods were introduced for computing the…

This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…

In this paper, we propose two monolithic fully discrete finite element methods for fluid-structure interaction (FSI) based on a novel Piola-type Arbitrary Lagrangian-Eulerian (ALE) mapping. For the temporal discretization, we apply the…

A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…

We design a monotone meshfree finite difference method for linear elliptic equations in the non-divergence form on point clouds via a nonlocal relaxation method. The key idea is a novel combination of a nonlocal integral relaxation of the…

We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We…

Harmonic stator-rotor coupling offers a promising approach for the interconnection of rotating subsystems in the simulation of electric machines. This paper studies the stability of discretization schemes based on harmonic coupling in the…

This paper presents efficient data structures for the implementation of matrix-free finite element methods on block-structured, hybrid tetrahedral grids. It provides a complete categorization of all geometric sub-objects that emerge from…