Related papers: Diagonalization-based preconditioners and generali…
We use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward…
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as…
This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained…
We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time dependent) Dirichlet…
PARyOpt is a python based implementation of the Bayesian optimization routine designed for remote and asynchronous function evaluations. Bayesian optimization is especially attractive for computational optimization due to its low cost…
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…
Evolutionary deep neural networks have emerged as a rapidly growing field of research. This paper studies numerical integrators for such and other classes of nonlinear parametrizations $ u(t) = \Phi(\theta(t)) $, where the evolving…
This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…
We consider the initial-boundary value problem for a quasilinear time-fractional diffusion equation, and develop a fully discrete solver combining the parareal algorithm in time with a L1 finite-difference approximation of the Caputo…
In this paper, we propose a direct parallel-in-time (PinT) algorithm for time-dependent problems with first- or second-order derivative. We use a second-order boundary value method as the time integrator that leads to a tridiagonal time…
To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a…
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…
This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation…
We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…
This work proposes a data-driven method for enabling the efficient, stable time-parallel numerical solution of systems of ordinary differential equations (ODEs). The method assumes that low-dimensional bases that accurately capture the time…
The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…