Computer Aided Design

Engineering

Boundary (topology)

Spline (mechanical)

Boundary value problem

Applied mathematics

Operating system

Computer science

Finite element method

Collocation (remote sensing)

Singular boundary method

Mathematics

Mathematical analysis

Boundary element method

Isogeometric analysis

Structural engineering

Engineering drawing

Machine learning

Computer Methods in Applied Mechanics and Engineering

An isogeometric boundary element method based on T-splines is used to simulate acoustic phenomena. We restrict our developments to low-frequency problems to establish the fundamental properties of the proposed approach. Using T-splines, the computer aided design (CAD) and boundary element analysis are integrated without recourse to geometry clean-up or mesh generation. A regularized Burton–Miller formulation is used resulting in integrals which are at most weakly singular. We employ a collocation-based approach to generate the linear system of equations. The method is verified against closed-form solutions and direct comparisons are made with conventional Lagrangian discretizations. It is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the T-spline. The method is then applied to a real-world application to illustrate the potential for integrated engineering design and analysis.

Acoustic isogeometric boundary element analysis