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Scaled boundary isogeometric analysis for electrostatic problems. (English) Zbl 1403.78027

Summary: The scaled boundary isogeometric analysis (SBIGA) is a novel semi-analytical technique, combing the advantages of the scaled boundary finite element method and the isogeometric analysis. In this paper, SBIGA is firstly exploited to solve electrostatic problems. According to the Laplace equation of electrostatic problems, the derivations and solutions of SBIGA equations for bounded domain and open domain problems are presented in details. A mortar method is employed to couple the solution on different subdomains, when the electrostatic problems with inhomogeneous media or complex boundaries which cannot be described by a single NURBS patch or cannot satisfy the scaling requirement in SBIGA. The mortar-based SBIGA can retain the flexibility of interface meshes compared with strong coupling methods. A condensation scheme is exploited to treat system equation in the analysis. Several numerical examples confirm the effectiveness, accuracy and convergence properties of SBIGA and the mortar-based SBIGA in solving electrostatic problems.

MSC:

78M15 Boundary element methods applied to problems in optics and electromagnetic theory
65N38 Boundary element methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
78M25 Numerical methods in optics (MSC2010)
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