相关论文: Certified Reduced Basis Method for Affinely Parame…

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are…

In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. They are generated from a tensor-product spline space by…

We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions of the parametric geometry diminish as the singularity is…

In this article we suggest two discretization methods based on isogeometric analysis (IGA) for planar linear elasticity. On the one hand, we apply the well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a…

One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…

To find consistent initial data points for a system of differential-algebraic equations, requires the identification of its missing constraints. An efficient class of structural methods exploiting a dependency graph for this task was…

Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…

In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The essential ingredients of the methodology are: a Galerkin…

We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint…

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…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

The analysis of electromagnetic scattering in the isogeometric analysis (IGA) framework based on Loop subdivision has long been restricted to simply-connected geometries. The inability to analyze multiply-connected objects is a glaring…

We introduced the package/subsystem GeoGebra Discovery to GeoGebra which supports the automated proving or discovering of elementary geometry inequalities. In this case study, for inequality exploration problems related to isosceles and…

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…

Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks…

We present an open-source Python framework for the shape optimization of complex shell structures using isogeometric analysis (IGA). IGA seamlessly integrates computer-aided design (CAD) and analysis models by employing non-uniform rational…

In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…

The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from…

In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints and bilateral parameter constraints. The approach employs successively enriched Reduced…

We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…