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Isogeometric analysis in BIE for 3-D potential problem. (English) Zbl 1352.65585
Summary: The isogeometric analysis is introduced in the Boundary Integral Equation (BIE) for solution of 3-D potential problems. In the solution, B-spline basis functions are employed not only to construct the exact geometric model but also to approximate the boundary variables. And a new kind of B-spline function, i.e., local bivariate B-spline function, is deducted, which is further applied to reduce the computation cost for analysis of some special geometric models, such as a sphere, where large number of nearly singular and singular integrals will appear. Numerical tests show that the new method has good performance in both exactness and convergence.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)
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