Related papers: Classical Optimal Designs for Stationary Diffusion…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the…
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…
This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the…
We propose a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of…
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…
This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple,…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
This paper is concerned with the optimized Schwarz waveform relaxation method and Ventcel transmission conditions for the linear advection-diffusion equation. A mixed formulation is considered in which the flux variable represents both…