相关论文: Multiplicative, Additive and Restricted Additive O…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
In this work the Lippmann-Schwinger equation is used to model seismic waves in strongly scattering acoustic media. We consider the Helmholtz equation, which is the scalar wave equation in the frequency domain with constant density and…
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…
In the present work, we study and analyze an efficient iterative coupling method for a dimensionally heterogeneous problem . We consider the case of 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…
We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose a new variant of the Optimized Schwarz Method (OSM) that can…
We consider an automatic construction of locally optimal preconditioners for positive definite linear systems. To achieve this goal, we introduce a differentiable loss function that does not explicitly include the estimation of minimal…
Classically transmission conditions between subdomains are optimized for a simplified two subdomain decomposition to obtain optimized Schwarz methods for many subdomains. We investigate here if such a simplified optimization suffices for…
We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the…
This paper is concerned with the existence and regularity of mininizers as well as of corresponding multipliers to an optimal control problem governed by semilinear elliptic equations, in which mixed pointwise control-state constraints are…
We present a simple way to discretize and precondition mixed variational formulations. Our theory connects with, and takes advantage of, the classical theory of symmetric saddle point problems and the theory of preconditioning symmetric…
Mixed integer predictive control deals with optimizing integer and real control variables over a receding horizon. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this…
Wave propagation problems governed by the Helmholtz equation remain among the most challenging in scientific computing, due to their indefinite nature. Domain decomposition methods with spectral coarse spaces have emerged as some of the…
Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…
This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive definite (SPD) matrices. For those matrices, the coarse space…
Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…
Schwarz methods are attractive parallel solvers for large scale linear systems obtained when partial differential equations are discretized. For hybridizable discontinuous Galerkin (HDG) methods, this is a relatively new field of research,…