Publications de Bernard Kapidani

Tree–cotree-based tearing and interconnecting for 3D magnetostatics: A dual–primal approach

The simulation of electromagnetic devices with complex geometries and large-scale discrete systems benefits from advanced computational methods like IsoGeometric Analysis and Domain Decomposition. In this paper, we employ both concepts in an Isogeometric T ...

2025

Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems

Bernard Kapidani

Common formulations of the eddy current problem involve either vector or scalar potentials, each with its own advantages and disadvantages. An impasse arises when using scalar potential-based formulations in the presence of conductors with non-trivial topo ...

2024

Mass lumping the dual cell method to arbitrary polynomial degree for acoustic and electromagnetic waves

Bernard Kapidani

We present a fundamental improvement of a high polynomial degree time domain cell method recently introduced by the last three authors. The published work introduced a method featuring block-diagonal system matrices where the block size and conditioning sc ...

2024

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

Rafael Vazquez Hernandez, Bernard Kapidani

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

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

Rafael Vazquez Hernandez, Bernard Kapidani

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

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

Rafael Vazquez Hernandez, Bernard Kapidani

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

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

Rafael Vazquez Hernandez, Bernard Kapidani

2022

An arbitrary-order Cell Method with block-diagonal mass-matrices for the time-dependent 2D Maxwell equations

Bernard Kapidani

We introduce a new numerical method for the time-dependent Maxwell equations on unstructured meshes in two space dimensions. This relies on the introduction of a new mesh, which is the barycentric-dual cellular complex of the starting simplicial mesh, and ...

2021