Rafael Vazquez Hernandez

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 ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

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

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 ...

2023

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

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 ...

2023

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

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 ...

2022

Mathematical Foundations of Adaptive Isogeometric Analysis

Ondine Gabrielle Chanon, Annalisa Buffa, Rafael Vazquez Hernandez

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 ...

SPRINGER2022

Adaptive analysis-aware defeaturing

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 ...

2022

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

Ondine Gabrielle Chanon, Annalisa Buffa, Rafael Vazquez Hernandez

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 ...

Institute of Electrical and Electronics Engineers2022

An a posteriori error estimator for isogeometric analysis on trimmed geometries

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 ...

2022

High Order Geometric Methods With Splines: An Analysis of Discrete Hodge-Star Operators

2022

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

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 ...

2021

Hierarchical B-spline complexes of discrete differential forms

In this paper, we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of problems arising in electromagnetics and uid mechanics. We de ...

2020

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these result ...

Springer2020

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

Annalisa Buffa, Riccardo Puppi, Rafael Vazquez Hernandez

2020

A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries

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 ...

2020

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

Annalisa Buffa, Pablo Antolin Sanchez, Luca Coradello, Rafael Vazquez Hernandez

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 ...

2020

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

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 ...

2020

Isogeometric Mortar Coupling for Electromagnetic Problems

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 ...

2020

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview