Related papers: A dimension-oblivious domain decomposition method …
The aim of this paper is twofold. On the one hand, we test numerically the performance of mixed virtual elements in three dimensions for the first time in the literature to solve the mixed formulation of three-dimensional elliptic equations…
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…
We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. The…
In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…
We introduce and analyze a Nitsche-based domain decomposition method for the solution of hypersingular integral equations. This method allows for discretizations with non-matching grids without the necessity of a Lagrangian multiplier, as…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The convergence analysis is established for the decomposition of the…
This paper proposes novel computational multiscale methods for linear second-order elliptic partial differential equations in nondivergence-form with heterogeneous coefficients satisfying a Cordes condition. The construction follows the…
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…
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…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
This paper shows how partial differential problems can be solved thanks to cellular computing and an adaptation of the Least Squares Finite Elements Method. As cellular computing can be implemented on distributed parallel architectures,…
In this paper, a new iterative two-level algorithm is presented for solving the finite element discretization for nonsymmetric or indefinite elliptic problems. The iterative two-level algorithm uses the same coarse space as the traditional…
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
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…
The DD-CPM software library provides a set of tools for the discretization and solution of problems arising from the closest point method (CPM) for partial differential equations on surfaces. The solvers are built on top of the well-known…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…