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As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes can be a…
A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…
This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order…
High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to low-order, matrix-based simulations, in particular in porous…
We consider a space-time variational formulation of parabolic initial-boundary value problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation. This variational setting is the starting point for the space-time…
This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
We present a finite element method for the incompressible Navier--Stokes problem that is locally conservative, energy-stable and pressure-robust on time-dependent domains. To achieve this, the space--time formulation of the Navier--Stokes…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
The aim of this paper is to apply a high-order discontinuous-in-time scheme to second-order hyperbolic partial differential equations (PDEs). We first discretize the PDEs in time while keeping the spatial differential operators…
In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…
We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preu{\ss} (SIAM J. Sci. Comput.…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
We present a monolithic $hp$ space-time multigrid method for tensor-product space-time finite element discretizations of the Stokes equations. Geometric and polynomial coarsening of the space-time mesh is performed, and the entire algorithm…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…
In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…
We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a…
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…