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Acceleration of isogeometric boundary element analysis through a black-box fast multipole method. (English) Zbl 1403.65228
Summary: This work outlines the use of a black-box fast multipole method to accelerate the far-field computations in an isogeometric boundary element method. The present approach makes use of T-splines to discretise both the geometry and analysis fields allowing a direct integration of CAD and analysis technologies. A black-box fast multipole method of \(O(N)\) complexity is adopted that minimises refactoring of existing boundary element codes and facilitates the use of different kernels. This paper outlines an algorithm for implementing the open-source black-box fast multipole method BBFMM3D within an existing isogeometric boundary element solver, but the approach is general in nature and can be applied to any boundary element surface discretisation. The \(O(N)\) behaviour of the approach is validated and compared against a standard direct solver. Finally, the ability to model large models of arbitrary geometric complexity directly from CAD models is demonstrated for potential problems.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
Software:
Trilinos
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