Related papers: A parallel domain decomposition method for solving…
We show how to solve hyperbolic equations numerically on unbounded domains by compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate…
As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…
In this article we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
We show how the newly developed method of Periodic Unfolding on Riemannian manifolds can be applied to PDE problems: We consider the homogenization of an elliptic model problem. In the limit, we obtain a generalization of the well-known…
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…
In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic…
We introduce an iterative method to prove the existence and uniqueness of the complex-valued nonlinear elliptic PDE of the form $ -\Delta u + F(u) = f $ with Dirichlet or Neumann boundary conditions on a precompact domain $ \Omega \subset…
In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
In this paper we design an iterative domain decomposition method for free boundary problems with nonlinear flux jump condition. Our approach is related to damped Newton's methods. The proposed scheme requires, in each iteration, the…
In this paper we use a natural iteration technique to prove existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to…
In this paper we propose new insights and ideas to set up quantitative boundary estimates for solutions to Dirichlet problem of a class of fully non-linear elliptic equations on compact Hermitian manifolds with real analytic Levi flat…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold.…