相关论文: A robust two-level overlapping preconditioner for …
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of…
We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level…
Modeling subsurface fluid flow in porous media is crucial for applications such as oil and gas exploration. However, the inherent heterogeneity and multi-scale characteristics of these systems pose significant challenges in accurately…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A crucial challenge is then that the solutions of the two…
Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than preconditioners based on incomplete block factorizations. Lower…
We propose a novel universal construction of two-level overlapping Schwarz preconditioners for $2m$th-order elliptic boundary value problems, where $m$ is a positive integer. The word "universal" here signifies that the coarse space…
We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
Coupled systems of free flow and porous media arise in a variety of technical and environmental applications. For laminar flow regimes, such systems are described by the Stokes equations in the free-flow region and Darcy's law in the porous…
The discretization of certain integral equations, e.g., the first-kind Fredholm equation of Laplace's equation, leads to symmetric positive-definite linear systems, where the coefficient matrix is dense and often ill-conditioned. We…
In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the…
Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this…
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…
We propose an augmented Lagrangian preconditioner for a three-field stress-velocity-pressure discretization of stationary non-Newtonian incompressible flow with an implicit constitutive relation of power-law type. The discretization…
A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…
Predicting the flow of non-Newtonian fluids in porous structure is still a challenging issue due to the interplay betwen the microscopic disorder and the non-linear rheology. In this letter, we study the case of an yield stress fluid in a…
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…
Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model…