Rafael Vazquez Hernandez

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We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splin ...

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer-aided design, which generates meshes that are unfitted with the described physical object. T ...

In this work, isogeometric mortaring is used for the simulation of a six-pole permanent magnet synchronous machine. Isogeometric mortaring is especially well suited for the efficient computation of rotating electric machines, as it allows for an exact geom ...

We present the construction of additive multilevel preconditioners, also known as BPX preconditioners, for the solution of the linear system arising in isogeometric adaptive schemes with (truncated) hierarchical B-splines. We show that the locality of hier ...

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depen ...

This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of ...

The construction of suitable mesh configurations for spline models that provide local refinement capabilities is one of the fundamental components for the analysis and development of adaptive isogeometric methods. We investigate the design and implementati ...

The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined on two-dimensiona ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10, 12, 11], optimal convergence rates of the AIGM can be proved when suitable approximation cla ...

When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribu ...

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible ...

Adaptive isogeometric methods for the solution of partial diifferential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical spline ...

Trimming is a common operation in computer aided design and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming, the geometric description of the patch remains ...

We present an adaptive scheme for isogeometric phase-field modeling, to perform suitably graded hierarchical refinement and coarsening on both single- and multi-patch geometries by considering truncated hierarchical spline constructions which ensure C1 con ...

This paper discusses and analyzes two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretized by either Nédélec-type polynomial finite elements or spline-based isogeometric analysis. The first approach ...

Rafael Vazquez Hernandez

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An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Torque Computation With the Isogeometric Mortar Method for the Simulation of Electric Machines

BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines

Adaptive analysis-aware defeaturing

Mathematical Foundations of Adaptive Isogeometric Analysis

Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines

Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach

An equilibrated flux a posteriori error estimator for defeaturing problems

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains

Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries

A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries

Adaptive isogeometric phase-field modeling of the Cahn-Hilliard equation: Suitably graded hierarchical refinement and coarsening on multi-patch geometries

Isogeometric Mortar Coupling for Electromagnetic Problems

BPX preconditioners for isogeometric analysis using analysis-suitable T-splines

ADAPTIVE ISOGEOMETRIC METHODS WITH HIERARCHICAL SPLINES: AN OVERVIEW