A three-grid high-order immersed finite element method for the analysis of CAD models

The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an efficient, robust, high-order immersed finite element method for complex CAD models. Our approach relies on three adaptive structured grids: a geometry grid for representing the implicit geometry, a finite element grid for discretising physical fields and a quadrature grid for evaluating the finite element integrals. The geometry grid is a sparse VDB (Volumetric Dynamic B+ tree) grid that is highly refined close to physical domain boundaries. The finite element grid consists of a forest of octree grids distributed over several processors, and the quadrature grid in each finite element cell is an octree grid constructed in a bottom-up fashion. The resolution of the quadrature grid ensures that finite element integrals are evaluated with sufficient accuracy and that any sub-grid geometric features, like small holes or corners, are resolved up to a desired resolution. The conceptual simplicity and modularity of our approach make it possible to reuse open-source libraries, i.e. openVDB and p4est for implementing the geometry and finite element grids, respectively, and BDDCML for iteratively solving the discrete systems of equations in parallel using domain decomposition. We demonstrate the efficiency and robustness of the proposed approach by solving the Poisson equation on domains described by complex CAD models and discretised with tens of millions of degrees of freedom. The solution field is discretised using linear and quadratic Lagrange basis functions

Quantitative analysis of chloroplast protein targeting

This thesis presents the first use of the Partition of Unity Method in quantifying the spatio-temporal dynamics of a fluorescent protein targeted to the chloroplast twin-arginine translocation pathway. The fluorescence loss in photobleaching technique is applied in a modified fashion to the measurement of substrate mobilities in the chloroplast stroma. Our in vivo results address the two suggested protein targeting mechanisms of membrane-binding before lateral movement to the translocon and direct binding to the translocon. A high performance computing C/C++ implementation of the Partition of Unity Method is used to perform simulations of fluoresence loss in photobleaching and allow a compelling comparison to photobleaching data series. The implementation is both mesh-free and particle-less

Engineering Analysis in Imprecise Geometric Models

Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergenc

Quantitative analysis of chloroplast protein targeting

This thesis presents the first use of the Partition of Unity Method in quantifying the spatio-temporal dynamics of a fluorescent protein targeted to the chloroplast twin-arginine translocation pathway. The fluorescence loss in photobleaching technique is applied in a modified fashion to the measurement of substrate mobilities in the chloroplast stroma. Our in vivo results address the two suggested protein targeting mechanisms of membrane-binding before lateral movement to the translocon and direct binding to the translocon. A high performance computing C/C++ implementation of the Partition of Unity Method is used to perform simulations of fluoresence loss in photobleaching and allow a compelling comparison to photobleaching data series. The implementation is both mesh-free and particle-less.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council (EPSRC) (EP/C512863/1), Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC) (BB/C00437X/1)GBUnited Kingdo