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• W210739001 abstract "The first goal of this thesis is the design of SciPAL (Scientific and Parallel AlgorithmsLibrary), a C++-based and operating-system-independent library. The core of SciPAL is a domain-specific embedded language for dense and sparse linear algebrawhich is presented in chapter 1. Chapter 2 shows that by using SciPAL, algorithmscan be stated in a mathematically intuitive, unified way in terms of matrix and vectoroperations. The resulting rapid prototyping capabilities are discussed by using LUfactorization and principal component analysis as example. SciPAL ports the mostfrequently used linear algebra classes of the widely used finite element library deal.IIto CUDA (NVidia’s extension of the programming language C for programming theirGPUs). Thereby, simulation frameworks based on deal.II can easily be adapted toGPU-based computing. Besides adding a user-friendly API to any BLAS SciPAL particularlyaims at simplifying the usage of NVidia’s CUBLAS, especially the issues ofdata transfer arising from CUDA’s distributed memory programming model. Chapter 3closes the first part with a brief discussion of the necessary steps to solve sparse,unstructured linear systems.The second part of this thesis is a collection of various examples which started asprojects based on deal.II and at some point profit from being moved to the GPU. Theyare drawn from the field of neuroscience, enginering of indoor airflow, quantum transportin semiconductor heterostructures and structure-function interaction of proteins.Chapter 4 contributes to the interactive stimulation of light-sensitive neurons byevaluating the efficiency of existing algorithms and their speedup by CUDA.The accurate numerical prediction of indoor airflows for building configurations ofpractical relevance is of paramount importance for the energy-efficient design of modernbuildings. Chapter 5 discusses CUDA-based preconditioning for indoor airflowand the technical implications for existing codes written for the numerical solution ofthe underlying Reynolds-averaged Navier-Stokes equations.Chapter 6 focuses on the main issues of designing proper boundary conditions forfinite element simulations of quantum transport in the Landauer-B¨ uttiker picture. Thesimulation of a two-dimensional electron gas for a given set of model parameters isnot a big deal. The difficult part is an accurate formulation of transparent boundaryconditions needed to truncate the source and drain leads to a finite length.The formulation of a GPU-based framework for quantum wave-packet dynamics inchapter 7 is straightforward if formulated in terms of matrix-vector products and is anexample for how to combine the topics of this thesis to solve a new problem class.The accurate simulation of single-molecule impedance spectroscopy of globularproteins must be done in 3D. Current theoretical models ignore boundary conditionsand the electro-chemical properties of ions completely. Chapter 8 introduces and improvedmodel based on the Poisson-Nernst-Plack equations. The physical propertiesare dominated by boundary layers and the discontinuity of the dielectric permittivityat the protein-solvent interface. The goal of the simulation is the determination of theelectro-diffusive fluxes in the solvent. To avoid the inclusion of the protein interior inthe simulation the Poisson problem in the protein interior is replaced by a boundaryvalueproblem leading to a FEM-BEM coupling. Since it is basically an elliptic problemmultigrid methods are particularly well-suited for its efficient solution." @default.
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• W210739001 title "CUDA-based Scientific Computing" @default.
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