Discontinuous Galerkin formulation for eddy-current problems
Purpose - The purpose of this paper is to describe a method for solving eddy current problems. Discontinuous basis functions are applied to conducting regions in eddy-current problems. This results in a block-diagonal mass matrix allowing explicit time stepping without having to solve large algebrai...
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| Veröffentlicht in: | Compel 2009-07, Vol.28 (4), p.1081-1090 |
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| creator | Außerhofer, S. Bíró, O. Preis, K. |
| description | Purpose - The purpose of this paper is to describe a method for solving eddy current problems. Discontinuous basis functions are applied to conducting regions in eddy-current problems. This results in a block-diagonal mass matrix allowing explicit time stepping without having to solve large algebraic systems.Design methodology approach - The effect of the basis functions in the conducting region is limited to the respective finite element. This yields to a block-diagonal mass matrix, whereas each block in this matrix belongs to one finite element. In the nonconducting region, traditional finite elements are used which leads to well-conditioned system matrices. For the two regions, different time steps are used.Findings - To avoid instability, a term which penalizes the tangential jump of the magnetic vector potential A has to be added. A value for weighting this term is suggested and tested on a simple two dimensional example.Originality value - The proposed method leads to a potentially fast method for solving eddy-current problems. |
| doi_str_mv | 10.1108/03321640910959125 |
| format | Article |
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Lowther, Oszkár</contributor><creatorcontrib>Außerhofer, S. ; Bíró, O. ; Preis, K. ; Bíró David A. Lowther, Oszkár</creatorcontrib><description>Purpose - The purpose of this paper is to describe a method for solving eddy current problems. Discontinuous basis functions are applied to conducting regions in eddy-current problems. This results in a block-diagonal mass matrix allowing explicit time stepping without having to solve large algebraic systems.Design methodology approach - The effect of the basis functions in the conducting region is limited to the respective finite element. This yields to a block-diagonal mass matrix, whereas each block in this matrix belongs to one finite element. In the nonconducting region, traditional finite elements are used which leads to well-conditioned system matrices. For the two regions, different time steps are used.Findings - To avoid instability, a term which penalizes the tangential jump of the magnetic vector potential A has to be added. 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In the nonconducting region, traditional finite elements are used which leads to well-conditioned system matrices. For the two regions, different time steps are used.Findings - To avoid instability, a term which penalizes the tangential jump of the magnetic vector potential A has to be added. A value for weighting this term is suggested and tested on a simple two dimensional example.Originality value - The proposed method leads to a potentially fast method for solving eddy-current problems.</abstract><cop>Bradford</cop><pub>Emerald Group Publishing Limited</pub><doi>10.1108/03321640910959125</doi><tpages>10</tpages></addata></record> |
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| subjects | Basis functions Boundary conditions Eddy currents Electric currents Galerkin method Magnetic fields Magnetic vector potentials Mass matrix Mathematical analysis Mathematical models Studies Time series |
| title | Discontinuous Galerkin formulation for eddy-current problems |
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