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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
Trilinos
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