Related papers: A diagonal sweeping domain decomposition method wi…
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by replacing sharp boundaries with a diffuse layer of thickness…
In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called…
In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on…
We study the Schwarz overlapping domain decomposition method applied to the Poisson problem on a special family of domains, which by construction consist of a union of a large number of fixed-size subdomains. These domains are motivated by…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…
In this paper, using the approximate particular solutions of Helmholtz equations, we solve the boundary value problems of Helmholtz equations by combining the methods of fundamental solutions (MFS) with the methods of particular solutions…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…
In this paper, we mainly discuss the convergence behavior of diffuse domain method (DDM) for solving semilinear parabolic equations with Neumann boundary condition defined in general irregular domains. We use a phasefield function to…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
The discretization of surface intrinsic PDEs has challenges that one might not face in the flat space. The closest point method (CPM) is an embedding method that represents surfaces using a function that maps points in the flat space to…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…
This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…
We consider one-level additive Schwarz domain decomposition preconditioners for the Helmholtz equation with variable coefficients (modelling wave propagation in heterogeneous media), subject to boundary conditions that include wave…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…