Compatible Discretizations for Maxwell's Equations with General Constitutive Laws Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/mp48sh202

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  • In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of a gradient are zero in a discrete setting. This compatibility of discretizations with the continuum Maxwell's equations guarantees that the numerical solutions are physically meaningful. We focus on the construction of a class of discretizations called Mimetic Finite Differences (MFD). The MFD method is a generalization of both staggered finite differences and mixed finite elements. We construct a parameterized family of MFD methods with equivalent formal order of accuracy. For time-dependent problems, we exploit this non-uniqueness by finding parameters which are optimal with respect to a certain criteria, for example, minimizing dispersion error. Dispersion error is a numerical artifact in which individual frequencies in a wave propagate at incorrect speeds; dominating the error in wave problems over long time propagation. The novelty of this work is the construction of an MFD discretization for Maxwell's equations which reduces dispersion error for transient wave propagation in materials that are modeled by a general class of linear constitutive laws. We provide theoretical analysis of these new discretizations including an analysis of stability and discrete divergence. We also provide numerical demonstrations to illustrate the theory. In addition to applications in the time domain we consider equilibrium Magnetohydrodynamic (MHD) generators. MHD generators extract power directly from a plasma by passing it through a strong magnetic field. Used as a topping cycle for traditional steam turbine generator, MHD offers a theoretical thermal efficiency of 60% compared to 40% of traditional systems. However, this technology has high life cycle costs due to equipment failure. One source of failure is arcing: the formation of high density currents which damage the generator. In this work we develop, analyze, and simulate a model of these generators. We use these simulations to show the viability of detecting electrical arcs by measurements of their magnetic fields outside of the generator.
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  • description.provenance : Approved for entry into archive by Julie Kurtz(julie.kurtz@oregonstate.edu) on 2016-06-14T17:51:53Z (GMT) No. of bitstreams: 2 McGregorDuncanA2016.pdf: 5467187 bytes, checksum: 57e2d3474e5c2b0d0e9dbd4375461f45 (MD5) license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5)
  • description.provenance : Submitted by Duncan McGregor (mcgregod) on 2016-06-13T20:46:39Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) McGregorDuncanA2016.pdf: 5739144 bytes, checksum: 94e8d8be2ad25ff6a099dc7b460df6f4 (MD5)
  • description.provenance : Rejected by Julie Kurtz(julie.kurtz@oregonstate.edu), reason: Rejecting to change on the Approval page, the Head of the Department to read - Chair of the Department of Mathematics. Also there is a blank page between the approval page and acknowledgement page, that should be removed. Once revised, log back into ScholarsArchive and go to the upload page. Replace the attached file with the revised file and resubmit. Thanks, Julie on 2016-06-13T21:56:48Z (GMT)
  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2016-06-14T21:19:21Z (GMT) No. of bitstreams: 2 McGregorDuncanA2016.pdf: 5467187 bytes, checksum: 57e2d3474e5c2b0d0e9dbd4375461f45 (MD5) license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5)
  • description.provenance : Rejected by Julie Kurtz(julie.kurtz@oregonstate.edu), reason: Everything looks good except on the Approval page you changed Chair to Head and it should read - Chair of the Department of Mathematics. Also there's a blank page after the approval page and before the Acknowledgement page that would be remove. Everything else is great and you made the deadline for a spring diploma. Once revised, log back into ScholarsArchive and go to the upload page. Replace the attached file with the revised file and resubmit. Thanks, Julie on 2016-06-12T01:33:28Z (GMT)
  • description.provenance : Submitted by Duncan McGregor (mcgregod) on 2016-06-11T00:09:54Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) McGregorDuncanA2016.pdf: 5739144 bytes, checksum: 94e8d8be2ad25ff6a099dc7b460df6f4 (MD5)
  • description.provenance : Submitted by Duncan McGregor (mcgregod) on 2016-06-14T02:55:32Z No. of bitstreams: 2 McGregorDuncanA2016.pdf: 5467187 bytes, checksum: 57e2d3474e5c2b0d0e9dbd4375461f45 (MD5) license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5)
  • description.provenance : Made available in DSpace on 2016-06-14T21:19:21Z (GMT). No. of bitstreams: 2 McGregorDuncanA2016.pdf: 5467187 bytes, checksum: 57e2d3474e5c2b0d0e9dbd4375461f45 (MD5) license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) Previous issue date: 2016-05-26

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