Related papers: A posteriori error analysis for Schwarz overlappin…
In this paper we revisit the Restricted Additive Schwarz method for solving discretized Helmholtz problems, using impedance boundary conditions on subdomains (sometimes called ORAS). We present this method in its variational form and show…
Abstract Interpretation approximates the semantics of a program by mimicking its concrete fixpoint computation on an abstract domain $\mathbb{A}$. The abstract (post-) fixpoint computation is classically divided into two phases: the…
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
A novel overlapping domain decomposition splitting algorithm based on a Crank-Nisolson method is developed for the stochastic nonlinear Schroedinger equation driven by a multiplicative noise with non-periodic boundary conditions. The…
Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…
Domain decomposition methods are widely used to solve sparse linear systems from scientific problems, but they are not suited to solve sparse linear systems extracted from integrated circuits. The reason is that the sparse linear system of…
In this paper we study convergence estimates for a multigrid algorithm with smoothers of successive subspace correction (SSC) type, applied to symmetric elliptic PDEs. First, we revisit a general convergence analysis on a class of multigrid…
The time harmonic Maxwell equations are of current interest in computational science and applied mathematics with many applications in modern physics. In this work, we present parallel finite element solver for the time harmonic Maxwell…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem instead of simply doing time stepping for computing European…
In a previous work, we introduced a discretization scheme for a constrained optimal control problem involving the fractional Laplacian. For such a control problem, we derived optimal a priori error estimates that demand the convexity of the…
We present a dimension-incremental method for function approximation in bounded orthonormal product bases to learn the solutions of various differential equations. Therefore, we decompose the source function of the differential equation…
While many methods exist to discretize nonlinear time-dependent partial differential equations (PDEs), the rigorous estimation and adaptive control of their discretization errors remains challenging. In this paper, we present a methodology…
We consider elliptic problems with complicated, discontinuous diffusion tensor $A_{\scriptscriptstyle 0} $. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…
In this paper, we propose a two-level overlapping additive Schwarz domain decomposition preconditioner for the symmetric interior penalty discontinuous Galerkin method for the second order elliptic boundary value problem with highly…
We present sharp estimates for the extremal eigenvalues of the Schur complements arising in saddle point problems. These estimates are derived using the auxiliary space theory, in which a given iterative method is interpreted as an…
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…
A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality…