388 research outputs found
Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings
We discuss aspects of implementation and performance of parallel iterative solution techniques applied to low Reynolds number flows around fixed and moving rigid bodies. The incompressible Navier-Stokes equations are discretised with Taylor-Hood finite elements in combination with a semi-implicit pressure-correction method. The resulting sequence of convection-diffusion and Poisson equations are solved with preconditioned Krylov subspace methods. To achieve overall scalability we consider new auxiliary algorithms for mesh handling and assembly of the system matrices. We compute the flow around a translating plate and a rotating insect wing to establish the scaling properties of the developed solver. The largest meshes have up to 132 × 10^6 hexahedral finite elements leading to around 3.3 × 10^9 unknowns. For the scalability runs the maximum core count is around 65.5 × 10^3. We find that almost perfect scaling can be achieved with a suitable Krylov subspace iterative method, like conjugate gradients or GMRES, and a block Jacobi preconditioner with incomplete LU factorisation as a subdomain solver. In addition to parallel performance data, we provide new highly-resolved computations of flow around a rotating insect wing and examine its vortex structure and aerodynamic loading.This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) through grant # EP/G008531/1. Additional support was provided by the Czech Science Foundation through grant 14-02067S, and by the Czech Academy of Sciences through RVO:67985840. The presented computations were performed on HECToR at the Edinburgh Parallel Computing Centre through PRACE-2IP (FP7 RI-283493).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.compfluid.2015.08.02
Manifold-based isogeometric analysis basis functions with prescribed sharp features
We introduce manifold-based basis functions for isogeometric analysis of
surfaces with arbitrary smoothness, prescribed continuous creases and
boundaries. The utility of the manifold-based surface construction techniques
in isogeometric analysis was demonstrated in Majeed and Cirak (CMAME, 2017).
The respective basis functions are derived by combining differential-geometric
manifold techniques with conformal parametrisations and the partition of unity
method. The connectivity of a given unstructured quadrilateral control mesh in
is used to define a set of overlapping charts. Each vertex with
its attached elements is assigned a corresponding conformally parametrised
planar chart domain in , so that a quadrilateral element is
present on four different charts. On the collection of unconnected chart
domains, the partition of unity method is used for approximation. The
transition functions required for navigating between the chart domains are
composed out of conformal maps. The necessary smooth partition of unity, or
blending, functions for the charts are assembled from tensor-product B-spline
pieces and require in contrast to earlier constructions no normalisation.
Creases are introduced across user tagged edges of the control mesh. Planar
chart domains that include creased edges or are adjacent to the domain boundary
require special local polynomial approximants. Three different types of chart
domain geometries are necessary to consider boundaries and arbitrary number and
arrangement of creases. The new chart domain geometries are chosen so that it
becomes trivial to establish local polynomial approximants that are always
continuous across tagged edges. The derived non-rational manifold-based
basis functions are particularly well suited for isogeometric analysis of
Kirchhoff-Love thin shells with kinks
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
Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures
A novel surface interrogation technique is proposed to compute the
intersection of curves with spline surfaces in isogeometric analysis. The
intersection points are determined in one-shot without resorting to a
Newton-Raphson iteration or successive refinement. Surface-curve intersection
is required in a wide range of applications, including contact, immersed
boundary methods and lattice-skin structures, and requires usually the solution
of a system of nonlinear equations. It is assumed that the surface is given in
form of a spline, such as a NURBS, T-spline or Catmull-Clark subdivision
surface, and is convertible into a collection of B\'ezier patches. First, a
hierarchical bounding volume tree is used to efficiently identify the B\'ezier
patches with a convex-hull intersecting the convex-hull of a given curve
segment. For ease of implementation convex-hulls are approximated with k-dops
(discrete orientation polytopes). Subsequently, the intersections of the
identified B\'ezier patches with the curve segment are determined with a
matrix-based implicit representation leading to the computation of a sequence
of small singular value decompositions (SVDs). As an application of the
developed interrogation technique the isogeometric design and analysis of
lattice-skin structures is investigated. The skin is a spline surface that is
usually created in a computer-aided design (CAD) system and the periodic
lattice to be fitted consists of unit cells, each containing a small number of
struts. The lattice-skin structure is generated by projecting selected lattice
nodes onto the surface after determining the intersection of unit cell edges
with the surface. For mechanical analysis, the skin is modelled as a
Kirchhoff-Love thin-shell and the lattice as a pin-jointed truss. The two types
of structures are coupled with a standard Lagrange multiplier approach
Topologically robust CAD model generation for structural optimisation
Computer-aided design (CAD) models play a crucial role in the design,
manufacturing and maintenance of products. Therefore, the mesh-based finite
element descriptions common in structural optimisation must be first translated
into CAD models. Currently, this can at best be performed semi-manually. We
propose a fully automated and topologically accurate approach to synthesise a
structurally-sound parametric CAD model from topology optimised finite element
models. Our solution is to first convert the topology optimised structure into
a spatial frame structure and then to regenerate it in a CAD system using
standard constructive solid geometry (CSG) operations. The obtained parametric
CAD models are compact, that is, have as few as possible geometric parameters,
which makes them ideal for editing and further processing within a CAD system.
The critical task of converting the topology optimised structure into an
optimal spatial frame structure is accomplished in several steps. We first
generate from the topology optimised voxel model a one-voxel-wide voxel chain
model using a topology-preserving skeletonisation algorithm from digital
topology. The weighted undirected graph defined by the voxel chain model yields
a spatial frame structure after processing it with standard graph algorithms.
Subsequently, we optimise the cross-sections and layout of the frame members to
recover its optimality, which may have been compromised during the conversion
process. At last, we generate the obtained frame structure in a CAD system by
repeatedly combining primitive solids, like cylinders and spheres, using
boolean operations. The resulting solid model is a boundary representation
(B-Rep) consisting of trimmed non-uniform rational B-spline (NURBS) curves and
surfaces
Transgenic Overexpression of LARGE Induces alpha-Dystroglycan Hyperglycosylation in Skeletal and Cardiac Muscle
Background: LARGE is one of seven putative or demonstrated glycosyltransferase enzymes defective in a common group of muscular dystrophies with reduced glycosylation of alpha-dystroglycan. Overexpression of LARGE induces hyperglycosylation of alpha-dystroglycan in both wild type and in cells from dystroglycanopathy patients, irrespective of their primary gene defect, restoring functional glycosylation. Viral delivery of LARGE to skeletal muscle in animal models of dystroglycanopathy has identical effects in vivo, suggesting that the restoration of functional glycosylation could have therapeutic applications in these disorders. Pharmacological strategies to upregulate Large expression are also being explored.Methodology/Principal Findings: In order to asses the safety and efficacy of long term LARGE over-expression in vivo, we have generated four mouse lines expressing a human LARGE transgene. On observation, LARGE transgenic mice were indistinguishable from the wild type littermates. Tissue analysis from young mice of all four lines showed a variable pattern of transgene expression: highest in skeletal and cardiac muscles, and lower in brain, kidney and liver. Transgene expression in striated muscles correlated with alpha-dystroglycan hyperglycosylation, as determined by immunoreactivity to antibody IIH6 and increased laminin binding on an overlay assay. Other components of the dystroglycan complex and extracellular matrix ligands were normally expressed, and general muscle histology was indistinguishable from wild type controls. Further detailed muscle physiological analysis demonstrated a loss of force in response to eccentric exercise in the older, but not in the younger mice, suggesting this deficit developed over time. However this remained a subclinical feature as no pathology was observed in older mice in any muscles including the diaphragm, which is sensitive to mechanical load-induced damage.Conclusions/Significance: This work shows that potential therapies in the dystroglycanopathies based on LARGE upregulation and alpha-dystroglycan hyperglycosylation in muscle should be safe
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
Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces
We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently refined control mesh. During iterative shape optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. This multiresolution approach provides a means for regularising the optimisation problem and prevents the appearance of sub-optimal jagged geometries with fine-scale oscillations. The finest control mesh for optimisation is chosen in accordance with the desired smallest feature size in the optimised geometry.
The proposed approach is applied to three optimisation examples, namely a catenary, a roof over a rectangular domain and a freeform architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries are investigated in detail
Fully probabilistic deep models for forward and inverse problems in parametric PDEs
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation leverages conventional PDE discretization techniques, deep neural networks, probabilistic modelling, and variational inference to assemble a fully probabilistic coherent framework. In the posited probabilistic model, both the forward and inverse maps are approximated as Gaussian distributions with a mean and covariance parameterized by deep neural networks. The PDE residual is assumed to be an observed random vector of value zero, hence we model it as a random vector with a zero mean and a user-prescribed covariance. The model is trained by maximizing the probability, that is the evidence or marginal likelihood, of observing a residual of zero by maximizing the evidence lower bound (ELBO). Consequently, the proposed methodology does not require any independent PDE solves and is physics-informed at training time, allowing the real-time solution of PDE forward and inverse problems after training. The proposed framework can be easily extended to seamlessly integrate observed data to solve inverse problems and to build generative models. We demonstrate the efficiency and robustness of our method on finite element discretized parametric PDE problems such as linear and nonlinear Poisson problems, elastic shells with complex 3D geometries, and time-dependent nonlinear and inhomogeneous PDEs using a physics-informed neural network (PINN) discretization. We achieve up to three orders of magnitude speed-up after training compared to traditional finite element method (FEM), while outputting coherent uncertainty estimates
Isogeometric analysis using manifold-based smooth basis functions
We present an isogeometric analysis technique that builds on manifold-based
smooth basis functions for geometric modelling and analysis. Manifold-based
surface construction techniques are well known in geometric modelling and a
number of variants exist. Common to all is the concept of constructing a smooth
surface by blending together overlapping patches (or, charts), as in
differential geometry description of manifolds. Each patch on the surface has a
corresponding planar patch with a smooth one-to-one mapping onto the surface.
In our implementation, manifold techniques are combined with conformal
parametrisations and the partition-of-unity method for deriving smooth basis
functions on unstructured quadrilateral meshes. Each vertex and its adjacent
elements on the surface control mesh have a corresponding planar patch of
elements. The star-shaped planar patch with congruent wedge-shaped elements is
smoothly parameterised with copies of a conformally mapped unit square. The
conformal maps can be easily inverted in order to compute the transition
functions between the different planar patches that have an overlap on the
surface. On the collection of star-shaped planar patches the partition of unity
method is used for approximation. The smooth partition of unity, or blending
functions, are assembled from tensor-product b-spline segments defined on a
unit square. On each patch a polynomial with a prescribed degree is used as a
local approximant. To obtain a mesh-based approximation scheme, the
coefficients of the local approximants are expressed in dependence of vertex
coefficients. This yields a basis function for each vertex of the mesh which is
smooth and non-zero over a vertex and its adjacent elements. Our numerical
simulations indicate the optimal convergence of the resulting approximation
scheme for Poisson problems and near optimal convergence for thin-plate and
thin-shell problems
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