Approximation and computation of the solution to the magnetosphere-ionosphere coupling equation via a mixed formulation

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dc.contributor.advisorKloucek, Petren_US
dc.contributor.advisorToffoletto, Frank R.en_US
dc.creatorWightman, Jennifer Leeen_US
dc.date.accessioned2009-06-04T08:38:00Zen_US
dc.date.available2009-06-04T08:38:00Zen_US
dc.date.issued2004en_US
dc.description.abstractThis study develops a numerical technique for the approximation of the magnetosphere-ionosphere (MI) coupling equation, which is a crucial step in the Rice Convection Model (RCM), a physical model that treats plasma in Earth's inner and middle magnetosphere via a multi-fluid approximation. The MI coupling equation is a second-order elliptic boundary value problem that describes conservation of current between the magnetosphere and the ionosphere. The current RCM solver is based on a finite difference scheme and produces unphysical results when the ionospheric conductance has large spatial gradients. We develop an alternative finite element approximation of the MI coupling equation, applying the method of fictitious domains to treat the high-latitude boundary condition along the immersed boundary Gamma, a boundary that varies in time and does not align with the computational grid. The result of using fictitious domains is a domain decomposition problem that we solve via a mixed finite element formulation. We compare both a nonconforming and conforming finite element approach within the framework of the mixed formulation. We are able to demonstrate that both the conforming and nonconforming methods generate solutions that are compatible with the current RCM solver when actual RCM data is used. Furthermore, we demonstrate on several analytic test examples that the finite element approximation is more accurate than the finite difference approximation. Therefore, we conclude that the finite element solver is more robust than the finite difference solver. In addition, we provide convergence results for the nonconforming approximation when the conductance coefficients are bounded and measurable, and we use spectral theory from the harmonic Steklov eigenproblem to derive a precise definition of the trace space on the interface Gamma. Our overall approximation technique is generalizable to a class of elliptic boundary value problems in which the boundary varies in time or does not align with a fixed grid. Finally, our numerical solver can be modified for use in the RCM-Jupiter that is currently being developed.en_US
dc.format.extent217 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2005 WIGHTMANen_US
dc.identifier.citationWightman, Jennifer Lee. "Approximation and computation of the solution to the magnetosphere-ionosphere coupling equation via a mixed formulation." (2004) Diss., Rice University. <a href="https://hdl.handle.net/1911/18837">https://hdl.handle.net/1911/18837</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18837en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.titleApproximation and computation of the solution to the magnetosphere-ionosphere coupling equation via a mixed formulationen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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