相关论文: A preconditioning strategy for linear systems aris…

The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While the theory and practice of such discretizations is now…

We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…

We study the convergence of iterative linear solvers for discontinuous Galerkin discretizations of systems of hyperbolic conservation laws with polygonal mesh elements compared with that of traditional triangular elements. We solve the…

We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate the well-posedness and convergence of the truncated Carleman…

We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…

This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…

We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton…

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational…

Embedded, or immersed, approaches have the goal of reducing to the minimum the computational costs associated with the generation of body-fitted meshes by only employing fixed, possibly Cartesian, meshes over which complex boundaries can…

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

We present scalable iterative solvers and preconditioning strategies for Hybridizable Discontinuous Galerkin (HDG) discretizations of partial differential equations (PDEs) on graphics processing units (GPUs). The HDG method is implemented…

We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…

We develop and analyze a class of structure-preserving discontinuous Galerkin schemes for the nonlinear Vlasov-Poisson-Fokker-Planck model, reformulated as a hyperbolic system through a Hermite expansion in the velocity variable. We…

We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial discretization with the backward Euler time-stepping scheme.…

Hybridizable discretizations allow for the elimination of local degrees-of-freedom leading to reduced linear systems. In this paper, we determine and analyse an approach to construct parameter-robust preconditioners for these reduced…

The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…

In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…

In this paper, we investigate a sequentially decoupled numerical method for solving the fully coupled quasi-static thermo-poroelasticity problems with nonlinear convective transport. The symmetric interior penalty discontinuous Galerkin…