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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | White, D.A. Fasenfest, B.J. |
| Copyright Year | 1965 |
| Abstract | In this paper, we present a low-rank QR method for evaluating the discrete Biot-Savart law. Our goal is to develop an algorithm that is easily implemented on parallel computers. It is assumed that the known current density and the unknown magnetic field are both expressed in a finite-element expansion, and we wish to compute the degrees-of-freedom (DOF) in the basis function expansion of the magnetic field. The matrix that maps the current DOF to the field DOF is full, but if the spatial domain is properly partitioned the matrix can be written as a block matrix, with blocks representing distant interactions being low rank and having a compressed QR representation. While an octree partitioning of the matrix may be ideal, for ease of parallel implementation, we employ a partitioning based on number of processors. The rank of each block (i.e., the compression) is determined by the specific geometry and is computed dynamically. In this paper, we provide the algorithmic details and present computational results for large-scale computations |
| Sponsorship | IEEE Magnetics Society |
| Starting Page | 1485 |
| Ending Page | 1488 |
| Page Count | 4 |
| File Size | 447799 |
| File Format | |
| ISSN | 00189464 |
| Volume Number | 43 |
| Issue Number | 4 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2007-04-01 |
| Publisher Place | U.S.A. |
| Access Restriction | One Nation One Subscription (ONOS) |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Finite element methods Magnetic fields Sparse matrices Current density Concurrent computing Magnetic flux Boundary conditions Computational efficiency Laboratories Computational geometry Maxwell's equations Biot–Savart law eddy currents electromagnetic diffusion |
| Content Type | Text |
| Resource Type | Article |
| Subject | Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering |
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