5 research outputs found
Boundary element based multiresolution shape optimisation in electrostatics
We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.Web of Science29759858
Boundary element based multiresolution shape optimisation in electrostatics
We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.We gratefully acknowledge the support provided by the EU commission through the FP7 Marie Curie IAPP project CASOPT (PIAP-GA-2008-230224). K.B. and F.C. thank for the additional support provided by EPSRC through #EP/G008531/1. J.Z. thanks for the support provided by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and by the project SPOMECH – Creating a Multidisciplinary R&D Team for Reliable Solution of Mechanical Problems, reg. no. CZ.1.07/2.3.00/20.0070 within the Operational Programme ‘Education for Competitiveness’ funded by the Structural Funds of the European Union and the state budget of the Czech Republic. Special thanks to Andreas Blaszczyk from the ABB Corporate Research Center Switzerland for fruitful discussions and for providing the industrial applications.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jcp.2015.05.01
Shape optimization of Stokesian peristaltic pumps using boundary integral methods
This article presents a new boundary integral approach for finding optimal
shapes of peristaltic pumps that transport a viscous fluid. Formulas for
computing the shape derivatives of the standard cost functionals and
constraints are derived. They involve evaluating physical variables (traction,
pressure, etc.) on the boundary only. By emplyoing these formulas in conjuction
with a boundary integral approach for solving forward and adjoint problems, we
completely avoid the issue of volume remeshing when updating the pump shape as
the optimization proceeds. This leads to significant cost savings and we
demonstrate the performance on several numerical examples
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
Shape optimisation with multiresolution subdivision surfaces and immersed finite elements
We develop a new optimisation technique that combines multiresolution
subdivision surfaces for boundary description with immersed finite elements for
the discretisation of the primal and adjoint problems of optimisation. Similar
to wavelets multiresolution surfaces represent the domain boundary using a
coarse control mesh and a sequence of detail vectors. Based on the
multiresolution decomposition efficient and fast algorithms are available for
reconstructing control meshes of varying fineness. During shape optimisation
the vertex coordinates of control meshes are updated using the computed shape
gradient information. By virtue of the multiresolution editing semantics,
updating the coarse control mesh vertex coordinates leads to large-scale
geometry changes and, conversely, updating the fine control mesh coordinates
leads to small-scale geometry changes. In our computations we start by
optimising the coarsest control mesh and refine it each time the cost function
reaches a minimum. This approach effectively prevents the appearance of
non-physical boundary geometry oscillations and control mesh pathologies, like
inverted elements. Independent of the fineness of the control mesh used for
optimisation, on the immersed finite element grid the domain boundary is always
represented with a relatively fine control mesh of fixed resolution. With the
immersed finite element method there is no need to maintain an analysis
suitable domain mesh. In some of the presented two- and three-dimensional
elasticity examples the topology derivative is used for creating new holes
inside the domain.The partial support of the EPSRC through grant # EP/G008531/1 and EC through Marie Curie Actions (IAPP) program CASOPT project are gratefully acknowledged.This is the final version of the article. It was first available from Elsevier via http://dx.doi.org/10.1016/j.cma.2015.11.01