Related papers: Coupling parallel adaptive mesh refinement with a …
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
In this paper, we present a robust distributed model predictive control (DMPC) scheme for dynamically decoupled nonlinear systems which are subject to state constraints, coupled state constraints and input constraints. In the proposed…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical…
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 this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating method, they have evolved into a rich family of algorithms that…
In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…
Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…
We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…
In this paper, we establish the convergence of the proximal alternating direction method of multipliers (ADMM) and block coordinate descent (BCD) for nonseparable minimization models with quadratic coupling terms. The novel convergence…
Balancing domain decomposition by constraints (BDDC) algorithms with adaptive primal constraints are developed in a concise variational framework for the weighted plane wave least-squares (PWLS) discritization of Helmholtz equations with…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…