Related papers: Monolithic two-level Schwarz preconditioner for Bi…
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…
We have given a novel formulation of the exact solutions for the lambda, vee and cascade three-level systems where the Hamiltonian of each configuration is expressed in the SU(3) basis. The solutions are discussed from the perspective of…
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…
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…
Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. The GenEO coarse space has been shown to lead to a fully robust two-level Schwarz preconditioner which scales well over…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of…
In this work, we present a hierarchical domain decomposition method for the multi-scale Boltzmann equation based on moment realizability matrices, a concept introduced by Levermore, Morokoff, and Nadiga in \cite{lev-mor-nad-1998}. This…
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…
In the context of non overlapping domain decomposition methods, several algebraic approximations of the Dirichlet-to-Neumann (DtN) map are proposed in [F. X. Roux, et. al. Algebraic approximation of Dirichlet- to-Neumann maps for the…
In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted explicit-implicit Euler time integration. We prove that the…
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission conditions, and exchange of information between subdomains…
We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$-dimensional triangulated surface $\Gamma$ in $\mathbb{R}^3$. We allow $\Gamma$ to…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…
In this paper, we revisit the patch solutions for a class of inviscid whole-space active scalar equations that interpolate between the 2D Euler equation and the $\alpha$-SQG equation. Compared with the 2D Euler equation in vorticity form,…
The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to…
We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To…
In this note, we consider preconditioned Krylov subspace methods for discrete fluid-structure interaction problems with a nonlinear hyperelastic material model and covering a large range of flows, e.g, water, blood, and air with highly…
We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all…