Related papers: Goal-Oriented Adaptivity and Multilevel Preconditi…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
We analyze a pointwise tracking multiobjective optimal control problem subject to the Poisson problem and bilateral control constraints. To approximate Pareto optimal points and the Pareto front numerically, we consider two different finite…
A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
The goal of this paper is to design optimal multilevel solvers for the finite element approximation of second order linear elliptic problems with piecewise constant coefficients on bisection grids. Local multigrid and BPX preconditioners…
Photo finishing tuning aims to automate the manual tuning process of the photo finishing pipeline, like Adobe Lightroom or Darktable. Previous works either use zeroth-order optimization, which is slow when the set of parameters increases,…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
In this paper, we solve the linearized Poisson-Boltzmann equation, used to model the electric potential of macromolecules in a solvent. We derive a corrected trapezoidal rule with improved accuracy for a boundary integral formulation of the…
In this paper we investigate adaptive discretization of the iteratively regularized Gauss- Newton method IRGNM. All-at-once formulations considering the PDE and the measurement equation simultaneously allow to avoid (approximate) solution…
We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…
This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…
This paper presents a PDE-based planar parameterization framework with support for Truncated Hierarchical B-Splines (THB-splines). For this, we adopt the a posteriori refinement strategy of Dual Weighted Residual and present several…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
An implicit method for the ohmic dissipation is proposed. The proposed method is based on the Crank-Nicolson method and exhibits second-order accuracy in time and space. The proposed method has been implemented in the SFUMATO adaptive mesh…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
In the last years decision-focused learning framework, also known as predict-and-optimize, have received increasing attention. In this setting, the predictions of a machine learning model are used as estimated cost coefficients in the…
In this paper, a multi-objective model-following control problem is solved using an observer-based adaptive learning scheme. The overall goal is to regulate the model-following error dynamics along with optimizing the dynamic variables of a…
In this paper we present a multigrid approach to solve the Poisson equation in arbitrary domain (identified by a level set function) and mixed boundary conditions. The discretization is based on finite difference scheme and ghost-cell…
We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the…