Numerical solution of PDEs in periodical domains
Numerical solution of PDEs in periodical domains
We present in this work two schemes of approximation for numerical solutions of PDEs. The first one is the maximum entropy method (max-ent) and the second one is the b-spline method. These methods let us impose a special kind of boundary conditions: periodic boundary conditions for unbounded domains. Some experiments need a large domain (or unbounded domain), however, this domain is divdided into some periodic cells. We develop a technique that let us simulate in the whole domain only doing a simulation in one cell. We apply this method for the resolution of second and fourth order problems (with periodic boundary conditions) like: Laplace, Kirchhoff plate and flexoelectricity.
Difference equations, Periodicity, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, Laplace, Difference equations, Partial--Numerical solutions, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Equacions diferencials parcials--solucions numèriques, Partial--Numerical solutions, Max-ent, Flexoelectricity, B-splines, Kirchhoff plate
Difference equations, Periodicity, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica, Laplace, Difference equations, Partial--Numerical solutions, Classificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems, Equacions diferencials parcials--solucions numèriques, Partial--Numerical solutions, Max-ent, Flexoelectricity, B-splines, Kirchhoff plate
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