Related papers: A Boundary-Layer Preconditioner for Singularly Per…
A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
Bounds are developed for the condition number of the linear finite element equations of an anisotropic diffusion problem with arbitrary meshes. They depend on three factors. The first, factor proportional to a power of the number of mesh…
Generally, discretization of partial differential equations (PDEs) creates a sequence of linear systems $A_k x_k = b_k, k = 0, 1, 2, ..., N$ with well-known and structured sparsity patterns. Preconditioners are often necessary to achieve…
This article investigates the numerical solution of the Diffusive Wave equation posed on domains containing a large number of polygonal perforations, motivated by urban flood modeling. Such geometries induce strong multiscale effects driven…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
This paper studies the spectral properties of large matrices and the preconditioning of linear systems, arising from the finite difference discretization of a time-dependent space-fractional diffusion equation with a variable coefficient…
A discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces which may…
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…
We extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces…
A parallel and nested version of a frequency filtering preconditioner is proposed for linear systems corresponding to diffusion equation on a structured grid. The proposed preconditioner is found to be robust with respect to jumps in the…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
In this paper we design, analyse and test domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations, namely for $\mathbf{H}(\mathbf{curl})$…
This manuscript is the second in a series presenting fast direct solution techniques for solving two-dimensional wave scattering problems from quasi-periodic multilayered structures. The fast direct solvers presented in the series are for…
In the present study, an advection-diffusion problem has been considered for the numerical solution. The continuum equation is discretized using both upwind and centered scheme. The linear system is solved using the ILU preconditioned…
We present a specific-purpose globalized and preconditioned Newton-CG solver to minimize a metric-aware curved high-order mesh distortion. The solver is specially devised to optimize curved high-order meshes for high polynomial degrees with…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…