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Full-Text Articles in Numerical Analysis and Computation
Eignefunctions For Partial Differential Equations On Two-Dimensional Domains With Piecewise Constant Coefficients, Abdullah Muheel Momit Aurko
Eignefunctions For Partial Differential Equations On Two-Dimensional Domains With Piecewise Constant Coefficients, Abdullah Muheel Momit Aurko
Master's Theses
In this thesis, we develop a highly accurate and efficient algorithm for computing the solution of a partial differential equation defined on a two-dimensional domain with discontinuous coefficients. An example of such a problem is for modeling the diffusion of heat energy in two space dimensions, in the case where the spatial domain represents a medium consisting of two different but homogeneous materials, with periodic boundary conditions.
Since diffusivity changes based on the material, it will be represented using a piecewise constant function, and this results in the formation of a complicated mathematical model. Such a model is impossible to …