Related papers: Multipreconditioning with directional sweeping met…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
This paper addresses several aspects of the linear Hybridizable Discontinuous Galerkin Method (HDG) for the Helmholtz equation with impedance boundary condition at high frequency. First, error estimates with explicit dependence on the wave…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
An overlapped continuous model framework, for the Helmholtz wave propagation problem in unbounded regions comprising bounded heterogeneous media, was recently introduced and analyzed by the authors ({\tt J. Comput. Phys., {\bf 403}, 109052,…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…
Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…
Getting standard multigrid to work efficiently for the high-frequency Helmholtz equation has been an open problem in applied mathematics for years. Much effort has been dedicated to finding solution methods which can use multigrid…
In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…
Time-harmonic wave propagation problems, especially those governed by Maxwell's equations, pose significant computational challenges due to the non-self-adjoint nature of the operators and the large, non-Hermitian linear systems resulting…
In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dimensions. While we solve the pure Helmholtz problem without…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
Operators with fractional perturbations are crucial components for robust preconditioning of interface-coupled multiphysics systems. However, in case the perturbation is strong, standard approaches can fail to provide scalable approximation…