Related papers: Two-component domain decomposition scheme with ove…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
To solve numerically boundary value problems for parabolic equations with mixed derivatives, the construction of difference schemes with prescribed quality faces essential difficulties. In parabolic problems, some possibilities are…
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…
In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…
We consider an overdetermined problem for a two phase elliptic operator in divergence form with piecewise constant coefficients. We look for domains such that the solution $u$ of a Dirichlet boundary value problem also satisfies the…
An efficient strategy to construct physics-based local surrogate models for parametric linear elliptic problems is presented. The method relies on proper generalized decomposition (PGD) to reduce the dimensionality of the problem and on an…
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
In this work we use algebraic dual representations in conjunction with domain decomposition methods for Darcy equations. We define the broken Sobolev spaces and their finite dimensional counterparts. In addition, a global trace space is…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
In this paper we propose on continuous level several domain decomposition methods to solve unilateral and ideal multibody contact problems of nonlinear elasticity. We also present theorems about convergence of these methods.
We develop a new compact scheme for second-order PDE (parabolic and Schr\"odinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary…
We give a factorization procedure for a strictly hyperbolic partial differential operator of second order with logarithmic slow scale coefficients. From this we can microlocally diagonalize the full wave operator which results in a coupled…
A fast method is presented for adaptive moving mesh generation in multi-dimensions using a domain decomposition parabolic Monge-Amp\`ere approach. The domain decomposition procedure employed here is non-iterative and involves splitting the…
We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share "nonlocal" interfaces of the size of…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…