Related papers: An IGA Framework for PDE-Based Planar Parameteriza…
Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…
We propose and analyze a domain decomposition solver for the biharmonic problem. The problem is discretized in a conforming way using multi-patch Isogeometric Analysis. As first step, we discuss the setup of a sufficiently smooth…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
Machine learning is a rapidly advancing field with diverse applications across various domains. One prominent area of research is the utilization of deep learning techniques for solving partial differential equations(PDEs). In this work, we…
Given the spline representation of the boundary of a three dimensional domain, constructing a volumetric spline parameterization of the domain (i.e., a map from a unit cube to the domain) with the given boundary is a fundamental problem in…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…
In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the…
This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when…
Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
The simulation of three dimensional magnetostatic problems plays an important role, for example when simulating synchronous electric machines. Building on prior work that developed a domain decomposition algorithm using isogeometric…
State of the art domain decomposition algorithms for large-scale boundary value problems (with $M\gg 1$ degrees of freedom) suffer from bounded strong scalability because they involve the synchronisation and communication of workers…
This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph $G$ and a set of terminal pairs $P$ and asks whether $G$ contains a set of pairwise edge-disjoint paths connecting every terminal…
This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric…
We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…