823 research outputs found
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces
We introduce a coupled finite and boundary element formulation for acoustic
scattering analysis over thin shell structures. A triangular Loop subdivision
surface discretisation is used for both geometry and analysis fields. The
Kirchhoff-Love shell equation is discretised with the finite element method and
the Helmholtz equation for the acoustic field with the boundary element method.
The use of the boundary element formulation allows the elegant handling of
infinite domains and precludes the need for volumetric meshing. In the present
work the subdivision control meshes for the shell displacements and the
acoustic pressures have the same resolution. The corresponding smooth
subdivision basis functions have the continuity property required for the
Kirchhoff-Love formulation and are highly efficient for the acoustic field
computations. We validate the proposed isogeometric formulation through a
closed-form solution of acoustic scattering over a thin shell sphere.
Furthermore, we demonstrate the ability of the proposed approach to handle
complex geometries with arbitrary topology that provides an integrated
isogeometric design and analysis workflow for coupled structural-acoustic
analysis of shells
Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
We present a new approach to three-dimensional electromagnetic scattering
problems via fast isogeometric boundary element methods. Starting with an
investigation of the theoretical setting around the electric field integral
equation within the isogeometric framework, we show existence, uniqueness, and
quasi-optimality of the isogeometric approach. For a fast and efficient
computation, we then introduce and analyze an interpolation-based fast
multipole method tailored to the isogeometric setting, which admits competitive
algorithmic and complexity properties. This is followed by a series of
numerical examples of industrial scope, together with a detailed presentation
and interpretation of the results
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