Finite element methods for Maxwell's equations.

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Computer-aided analysis of electronic circuits: Algorithms and computational techniques

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled, and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This article discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.

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DOLFIN: Automated finite element computing

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.

DOLFIN: Automated Finite Element Computing

Electric field calculations based on numerical methods and increasingly realistic head models are more and more used in research on Transcranial Magnetic Stimulation (TMS). However, they are still far from being established as standard tools for the planning and analysis in practical applications of TMS. Here, we start by delineating three main challenges that need to be addressed to unravel their full potential. This comprises (i) identifying and dealing with the model uncertainties, (ii) establishing a clear link between the induced fields and the physiological stimulation effects, and (iii) improving the usability of the tools for field calculation to the level that they can be easily used by non-experts. We then introduce a new version of our pipeline for field calculations (www.simnibs.org) that substantially simplifies setting up and running TMS and tDCS simulations based on Finite-Element Methods (FEM). We conclude with a brief outlook on how the new version of SimNIBS can help to target the above identified challenges.

Field modeling for transcranial magnetic stimulation: A useful tool to understand the physiological effects of TMS?

A general computer aided description environment for the treatment of discrete problems, based on a concise structure for both development and application levels, is described and applied to the finite element method. Its characteristics reveal its great ability to welcome in an evolutive way a wide range of physical models and numerical methods, with any coupling of them. It is therefore adapted to various activities, such as research, collaboration, education, training and industrial studies.

A general environment for the treatment of discrete problems and its application to the finite element method

Starting from the well known analytical formula for the eddy current losses in electrical steel laminations, saturation and edge effects are studied by means of 1D and 2D finite element models of a single lamination. A novel method for directly including the laminated core energy dissipation in a time stepped 2D model of a complete (rotating) machine is proposed. By way of example the method is applied to a tooth model with enforced flux waveforms.

Calculation of eddy currents and associated losses in electrical steel laminations

GetDP: a general environment for the treatment of discrete problems

The authors present a novel nonlinear homogenization technique for laminated iron cores in three-dimensional (3-D) finite-element (FE) models of electromagnetic devices. The technique takes into account the eddy current effects in the stacked core without the need of modeling all laminations separately. A nonlinear constitutive magnetic law is considered. The system of nonlinear algebraic equations obtained after time discretization is solved by means of the Newton-Raphson scheme. By way of validation, the method is applied to a 3-D FE model of a laminated ring core with toroidal coil

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A nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models

A method for defining global quantities related to fluxes and circulations is proposed in the frame of the finite element method. The definition is in perfect accordance with the discretized weak formulations of the problems. It therefore enables a natural coupling between local and global quantities in various formulations, while keeping a symmetrical matrix for the system, and then is open to the coupling of physical problems. Applications are given for electrostatics, magnetostatics and magnetodynamics.

Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics

Patrick Dular

Papers

A general environment for the treatment of discrete problems and its application to the finite element method

Calculation of eddy currents and associated losses in electrical steel laminations

GetDP: a general environment for the treatment of discrete problems

A nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models

Coupling of local and global quantities in various finite element formulations and its application to electrostatics, magnetostatics and magnetodynamics