Related papers: Optimality of multilevel preconditioners for local…
The relaxed micromorphic model is a generalized continuum model that is well-posed in the space $X = [H^1]^3 \times [H(\textrm{curl})]^3$. Consequently, finite element formulations of the model rely on $H^1$-conforming subspaces and…
In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…
In this work, we propose a novel diagonalization-based preconditioner for the all-at-once linear system arising from the optimal control problem of parabolic equations. The proposed preconditioner is constructed based on an…
This work investigates inexact block Schur complement preconditioning for linear poroelasticity problems discretized using a hybrid approach: Bernardi-Raugel elements for solid displacement and lowest-order weak Galerkin elements for fluid…
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from…
The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a given cubic pyramid into a conforming set of congruent…
The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on a Bakhvalov-type mesh is analyzed. The preconditioning technique is used to obtain the pointwise convergence uniform in…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
In this paper we are concerned with fast algorithms for the systems arising from the plane wave discretizations for two-dimensional Helmholtz equations with large wave numbers. We consider the plane wave weighted least squares (PWLS) method…
Local meshless methods using RBFs augmented with monomials have become increasingly popular, due to the fact that they can be used to solve PDEs on scattered node sets in a dimension-independent way, with the ability to easily control the…
To enhance the positioning and tracking performance of dynamic user equipment (UE) in wideband millimeter-wave (mmWave) systems, we propose a novel positioning error lower bound (PELB)-driven ping-pong positioning framework, where the base…
This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on $B^0_{p,1}$ penalty terms which yield estimators that are sparse with respect to a wavelet…
We present a weighted BFBT approximation (w-BFBT) to the inverse Schur complement of a Stokes system with highly heterogeneous viscosity. When used as part of a Schur complement-based Stokes preconditioner, we observe robust fast…
We consider space-time tracking optimal control problems for linear para\-bo\-lic initial boundary value problems that are given in the space-time cylinder $Q = \Omega \times (0,T)$, and that are controlled by the right-hand side…
For unconstrained control problems, a local convergence rate is established for an $hp$-method based on collocation at the Radau quadrature points in each mesh interval of the discretization. If the continuous problem has a sufficiently…
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
We consider multilevel decompositions of piecewise constants on simplicial meshes that are stable in $H^{-s}$ for $s\in (0,1)$. Proofs are given in the case of uniformly and locally refined meshes. Our findings can be applied to define…
Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be…