421 research outputs found
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
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
A low-rank isogeometric solver based on Tucker tensors
We propose an isogeometric solver for Poisson problems that combines i)
low-rank tensor techniques to approximate the unknown solution and the system
matrix, as a sum of a few terms having Kronecker product structure, ii) a
Truncated Preconditioned Conjugate Gradient solver to keep the rank of the
iterates low, and iii) a novel low-rank preconditioner, based on the Fast
Diagonalization method where the eigenvector multiplication is approximated by
the Fast Fourier Transform. Although the proposed strategy is written in
arbitrary dimension, we focus on the three-dimensional case and adopt the
Tucker format for low-rank tensor representation, which is well suited in low
dimension. We show in numerical tests that this choice guarantees significant
memory saving compared to the full tensor representation. We also extend and
test the proposed strategy to linear elasticity problems.Comment: 27 pages, 8 figure
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