Related papers: An Overlapping Domain Decomposition Preconditioner…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
The Dirichlet-Neumann method is a common domain decomposition method for nonoverlapping domain decomposition and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
We develop a nonoverlapping domain decomposition preconditioner for the $C^0$ interior penalty method, a discontinuous Galerkin method, for the biharmonic problem. The preconditioner is based on balancing domain decomposition by constraints…
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…
Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…
We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume potential in terms of the Green's function, we arrive at the…
We develop efficient and high-order accurate solvers for the Helmholtz equation on complex geometry. The schemes are based on the WaveHoltz algorithm which computes solutions of the Helmholtz equation by time-filtering solutions of the wave…
Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The…
We study a method based on Balancing Domain Decomposition by Constraints (BDDC) for a numerical solution of a single-phase flow in heterogenous porous media. The method solves for both flux and pressure variables. The fluxes are resolved in…
Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this…
Solving partial differential equations (PDEs) on complex domains can present significant computational challenges. The Diffuse Domain Method (DDM) is an alternative that reformulates the partial differential equations on a larger, simpler…
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…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
We propose domain decomposition preconditioners for the solution of an integral equation formulation of forward and inverse acoustic scattering problems with point scatterers. We study both forward and inverse problems and propose…
In this paper, a decentralized proximal method of multipliers (DPMM) is proposed to solve constrained convex optimization problems over multi-agent networks, where the local objective of each agent is a general closed convex function, and…
The time harmonic Maxwell equations are of current interest in computational science and applied mathematics with many applications in modern physics. In this work, we present parallel finite element solver for the time harmonic Maxwell…
We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…