Efficient modelling techniques for complicated boundary conditions applied to structured grids

Gersem, Herbert De; Wilke, Markus; Clemens, Markus; Weiland, Thomas

doi:10.1108/03321640410553337

Cited by 8 publications

(4 citation statements)

References 9 publications

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“…Choosing the anchor A ∈ A p,p (M 0 ) located at the T-junction, it is clear from (21) that ∂B A p,p ∂x is a linear combination of B A l p−1,p and B A r p−1,p , with A l , A r ∈ A p−1,p (M 1 1 ) as in Figure 12(b). Hence, ∂B A p,p ∂x ∈ T p−1,p (M 1 1 ) (see (50)), but since A l ∈ A p−1,p (M 0 ), we have ∂B A p,p ∂x ∈ T p−1,p (M 0 ). The argument is analogous for the partial derivative with respect to the y direction, with vertical T-junctions.…”

Section: Two-dimensional De Rham Complex With T-splines On the Paramementioning

confidence: 98%

“…In the case of finite elements this is not case (see e.g. [49], [50,51], [52] or [53] ) and, moreover, these features can hardly be obtained in conjunction with high-order finite element techniques. Discretization methods based on the use of both chain and cochain complexes in the framework of isogeometric methods are very promising and object of on-going research.…”

Section: Complex On the Parametric Domain ωmentioning

confidence: 99%

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Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Buffa

Sangalli

Vázquez

2014

Journal of Computational Physics

109

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In this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and, following the isogeometric paradigm, we map them on domains which are (piecewise) spline or NURBS geometries. We analyse their geometric structure, as related to the connectivity of the underlying mesh, and we give a physical interpretation of the fields degrees-of-freedom through the concept of control fields. The theory is then extended to the case of meshes with T-junctions, leveraging on the recent theory of T-splines. The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose.

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Section: Two-dimensional De Rham Complex With T-splines On the Paramementioning

confidence: 98%

Section: Complex On the Parametric Domain ωmentioning

confidence: 99%

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Buffa

Sangalli

Vázquez

2014

Journal of Computational Physics

109

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“…The following packages are associated with the problem definition step: bdrycond : In this package, boundary conditions are defined. Besides the standard Dirichlet and Neumann boundary conditions, also Robin, periodic, antiperiodic and floating boundary conditions are supported (De Gersem et al , 2004b). There is a container class that manages all boundary conditions of a problem and can apply them to the system of equations of the corresponding problem. excitation : In this package, excitations for problems are defined.…”

Section: Software Structurementioning

confidence: 99%

Pyrit: A finite element based field simulation software written in Python

Bundschuh,

Ruppert,

Späck-Leigsnering

2023

COMPEL

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Purpose The purpose of this paper is to present the freely available finite element simulation software Pyrit. Design/methodology/approach In a first step, the design principles and the objective of the software project are defined. Then, the software’s structure is established: The software is organized in packages for which an overview is given. The structure is based on the typical steps of a simulation workflow, i.e., problem definition, problem-solving and post-processing. State-of-the-art software engineering principles are applied to ensure a high code quality at all times. Finally, the modeling and simulation workflow of Pyrit is demonstrated by three examples. Findings Pyrit is a field simulation software based on the finite element method written in Python to solve coupled systems of partial differential equations. It is designed as a modular software that is easily modifiable and extendable. The framework can, therefore, be adapted to various activities, i.e., research, education and industry collaboration. Research limitations/implications The focus of Pyrit are static and quasistatic electromagnetic problems as well as (coupled) heat conduction problems. It allows for both time domain and frequency domain simulations. Originality/value In research, problem-specific modifications and direct access to the source code of simulation tools are essential. With Pyrit, the authors present a computationally efficient and platform-independent simulation software for various electromagnetic and thermal field problems.

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“…is built (Meyer, 2001). Application of this special projection operator within a preconditioned projected conjugate gradient method (PPCG) (De Gersem et al, 2004), yields a vector which lies in the kernel of W. Starting with x 0 that fulfills the linear constraints Wx 0 ¼ 0 the projector P ensures that the solution is found in the kernel of W. In the PPCG algorithm, K denotes the system matrix and f the right hand side of the linear equations in each stage of equation ( 7) and M the corresponding preconditioning matrix. The application of the projector g ¼ Pr is performed in two steps:…”

Section: Projection Techniques For Irregular Meshesmentioning

confidence: 99%

Error control schemes for adaptive time integration of magnetodynamic systems with variable spatial mesh resolution

Wimmer

Steinmetz

Clemens

2007

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -A combination of both time step adaptivity and spatial mesh adaptivity is presented for transient magneto-quasistatic fields. Design/methodology/approach -Error controlled time step adaptivity is achieved using an implicit integration scheme and the spatial mesh resolution is adapted in each time step in order to effectively resolve the appearing and disappearing local transient saturation effects and eddy current layers. Two spatial refinement strategies are considered, the red-green refinement leading to a regular mesh and the red refinement leading to an irregular mesh. Numerical results for 2d nonlinear magneto-dynamic problems are presented. Findings -An algorithm is proposed which computes the solution of a transient magnetostatic problem given a user prescribed error tolerance for the time stepping and the spatial refinement. The red refinement leading to irregular meshes requires projection techniques in the iterative conjugate gradient solver. However, the algorithm with red-green refinement turns out to perform faster since the projection is too expensive. Originality/value -The combination of error controlled time stepping and spatial adaptivity is firstly established in electromagnetic field computation.

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Efficient modelling techniques for complicated boundary conditions applied to structured grids

Cited by 8 publications

References 9 publications

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

Pyrit: A finite element based field simulation software written in Python

Error control schemes for adaptive time integration of magnetodynamic systems with variable spatial mesh resolution

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