Related papers: Nonconforming Schwarz-Spectral Element Methods For…
We propose two variants of the overlapping additive Schwarz method for the finite element discretiza- tion of the elliptic problem in 3D with highly heterogeneous coefficients. The methods are efficient and simple to construct using the…
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…
Semi-implicit semi-Lagrangian (SISL) methods are commonly used for the shallow water equations (SWE) because they allow for larger time steps than those permitted by the Courant-Friedrichs-Lewy (CFL) stability condition in Eulerian schemes.…
Highly resolved finite element simulations of a laser beam welding process are considered. The thermomechanical behavior of this process is modeled with a set of thermoelasticity equations resulting in a nonlinear, nonsymmetric saddle point…
We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all…
Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method…
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…
Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system…
The discretization of surface intrinsic elliptic partial differential equations (PDEs) poses interesting challenges not seen in flat space. The discretization of these PDEs typically proceeds by either parametrizing the surface,…
With recent advancements in computer hardware and software platforms, there has been a surge of interest in solving partial differential equations with deep learning-based methods, and the integration with domain decomposition strategies…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
This paper presents a semi-implicit spectral deferred correction (SDC) method for incompressible Navier-Stokes problems with variable viscosity and time-dependent boundary conditions. The proposed method integrates elements of velocity- and…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
In this paper, we consider an online basis enrichment mixed generalized multiscale method with oversampling, for solving flow problems in highly heterogeneous porous media. This is an exten- sion of the online mixed generalized multiscale…
Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, and it was observed that the classical Schwarz method can be convergent even without overlap in certain cases.…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
Scalar fields, such as stress or temperature fields, are often calculated in shape optimization and design problems in engineering. For complex problems where shapes have varying topology and cannot be parametrized, data-driven scalar field…
In this paper we introduce a new Schwarz framework and theory, based on the well-known idea of space decomposition, for nonsymmetric and indefinite linear systems arising from continuous and discontinuous Galerkin approximations of general…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…