Related papers: A mimetic spectral element solver for the Grad-Sha…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
The Volume-Averaged Navier-Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high-order finite element solver using both forms A and B of these equations.…
This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…
We present a variationally separable splitting technique for the generalized-$\alpha$ method for solving parabolic partial differential equations. We develop a technique for a tensor-product mesh which results in a solver with a linear cost…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve arbitrarily high-orders of convergence in terms of a…
One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…
Accurate and rapid simulation of the free boundary tokamak plasma equilibrium evolution is essential for modern plasma control, stability analysis, and scenario development. This paper presents the Free-Boundary Grad-Shafranov Evolutive…
We consider a space-time finite element method for the numerical solution of a distributed tracking-type optimal control problem subject to the heat equation with state constraints. The cost or regularization term is formulated in an…
We propose a spectral solver for the Poisson equation on a square domain, achieving optimal complexity through the ultraspherical spectral method and the alternating direction implicit (ADI) method. Compared with the state-of-the-art…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
We present a boundary integral equation solver for computing Taylor relaxed states in non-axisymmetric solid and shell-like toroidal geometries. The computation of Taylor states in these geometries is a key element for the calculation of…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…