Related papers: Overlapping Domain Decomposition Methods for Linea…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
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…
A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping source transfer domain decomposition method for layered medium, which is an extension of the source…
The transferable neural network (TransNet) is a two-layer shallow neural network with pre-determined and uniformly distributed neurons in the hidden layer, and the least-squares solvers can be particularly used to compute the parameters of…
We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…
In this paper, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The new method is an iterative two-scale method that uses a parareal-like update scheme in combination with…
Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling…
Cooperative Co-evolution, through the decomposition of the problem space, is a primary approach for solving large-scale global optimization problems. Typically, when the subspaces are disjoint, the algorithms demonstrate significantly both…
We present a domain decomposition-based deep learning method for solving elliptic and parabolic interface problems with discontinuous coefficients in two to ten dimensions. Our Multi-Activation Function (MAF) approach employs two…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
We consider a slightly subcritical elliptic system with Dirichlet boundary conditions and a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…
Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…
A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…
An accurate approximation of solutions to elliptic problems in infinite domains is challenging from a computational point of view. This is due to the need to replace the infinite domain with a sufficiently large and bounded computational…
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…