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

Attitudes politiques de Tunis dans le conflit entre Aragonais et Français en Sicile autour de 1282

International audienceSimulating the deformation of the human anatomy is a central element of Medical Image Computing and Computer Assisted Interventions. Such simulations play a key role in non-rigid registration, augmented reality, and several other applications. Although the Finite Element Method is widely used as a numerical approach in this area, it is often hindered by the need for an optimal meshing of the domain of interest. The derivation of meshes from imaging modalities such as CT or MRI can be cumbersome and time-consuming. In this paper we use the Immersed Boundary Method (IBM) to bridge the gap between these imaging modalities and the fast simulation of soft tissue deformation on complex shapes represented by a surface mesh directly retrieved from binary images. A high resolution surface, that can be obtained from binary images using a marching cubes approach, is embedded into a hexahedral simulation grid. The details of the surface mesh are properly taken into account in the hexahedral mesh by adapting the Mirtich integration method. In addition to not requiring a dedicated meshing approach, our method results in higher accuracy for less degrees of freedom when compared to other element types. Examples on brain deformation demonstrate the potential of our method

First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis

International audienceIn this work, we develop a specialized quadrature rule for trimmed domains , where the trimming curve is given implicitly by a real-valued function on the whole domain. We follow an error correction approach: In a first step, we obtain an adaptive subdivision of the domain in such a way that each cell falls in a pre-defined base case. We then extend the classical approach of linear approximation of the trimming curve by adding an error correction term based on a Taylor expansion of the blending between the linearized implicit trimming curve and the original one. This approach leads to an accurate method which improves the convergence of the quadrature error by one order compared to piecewise linear approximation of the trimming curve. It is at the same time efficient, since essentially the computation of one extra one-dimensional integral on each trimmed cell is required. Finally, the method is easy to implement, since it only involves one additional line integral and refrains from any point inversion or optimization operations. The convergence is analyzed theoretically and numerical experiments confirm that the accuracy is improved without compromising the computational complexity

Nuclear Outsourcing of RNA Interference Components to Human Mitochondria

MicroRNAs (miRNAs) are small non-coding RNAs that associate with Argonaute proteins to regulate gene expression at the post-transcriptional level in the cytoplasm. However, recent studies have reported that some miRNAs localize to and function in other cellular compartments. Mitochondria harbour their own genetic system that may be a potential site for miRNA mediated post-transcriptional regulation. We aimed at investigating whether nuclear-encoded miRNAs can localize to and function in human mitochondria. To enable identification of mitochondrial-enriched miRNAs, we profiled the mitochondrial and cytosolic RNA fractions from the same HeLa cells by miRNA microarray analysis. Mitochondria were purified using a combination of cell fractionation and immunoisolation, and assessed for the lack of protein and RNA contaminants. We found 57 miRNAs differentially expressed in HeLa mitochondria and cytosol. Of these 57, a signature of 13 nuclear-encoded miRNAs was reproducibly enriched in mitochondrial RNA and validated by RT-PCR for hsa-miR-494, hsa-miR-1275 and hsa-miR-1974. The significance of their mitochondrial localization was investigated by characterizing their genomic context, cross-species conservation and instrinsic features such as their size and thermodynamic parameters. Interestingly, the specificities of mitochondrial versus cytosolic miRNAs were underlined by significantly different structural and thermodynamic parameters. Computational targeting analysis of most mitochondrial miRNAs revealed not only nuclear but also mitochondrial-encoded targets. The functional relevance of miRNAs in mitochondria was supported by the finding of Argonaute 2 localization to mitochondria revealed by immunoblotting and confocal microscopy, and further validated by the co-immunoprecipitation of the mitochondrial transcript COX3. This study provides the first comprehensive view of the localization of RNA interference components to the mitochondria. Our data outline the molecular bases for a novel layer of crosstalk between nucleus and mitochondria through a specific subset of human miRNAs that we termed ‘mitomiRs’

A fixed-grid b-spline finite element technique for fluid-structure interaction

We present a fixed-grid finite element technique for fluid-structure interaction problems involving incompressible viscous flows and thin structures. The flow equations are discretised with isoparametric b-spline basis functions defined on a logically Cartesian grid. In addition, the previously proposed subdivision-stabilisation technique is used to ensure inf-sup stability. The beam equations are discretised with b-splines and the shell equations with subdivision basis functions, both leading to a rotation-free formulation. The interface conditions between the fluid and the structure are enforced with the Nitsche technique. The resulting coupled system of equations is solved with a Dirichlet-Robin partitioning scheme, and the fluid equations are solved with a pressure-correction method. Auxiliary techniques employed for improving numerical robustness include the level-set based implicit representation of the structure interface on the fluid grid, a cut-cell integration algorithm based on marching tetrahedra and the conservative data transfer between the fluid and structure discretisations. A number of verification and validation examples, primarily motivated by animal locomotion in air or water, demonstrate the robustness and efficiency of our approach. © 2013 John Wiley & Sons, Ltd

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 introducing new holes inside the domain. The merging or removing of holes is not considered

An unstructured immersed finite element method for nonlinear solid mechanics

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolation. For discretisation structured and unstructured background meshes with Lagrange basis functions are considered. We show numerically and analytically that the introduced cut-element stabilisation technique provides an effective bound on the size of the Nitsche parameters and, in turn, leads to well-conditioned system matrices. In addition, we introduce a novel approach for representing and analysing geometries with sharp features (edges and corners) using an implicit geometry representation. This allows the computation of typical engineering parts composed of solid primitives without the need of boundary-fitted meshes