Studies On Large Scale Structural Computations Based On Graphics Processing Units

Graphics processing units (GPUs) are powerful parallel processors, and genera l purposeGPU computations (GPGPU computations) are implemented in ma ny fields. In thisdissertation, OpenGL shading la nguage is used to compile GPU fragment programs, andGPUs are employed to accelera te the computations for large scale structures.GPGPU computations are described. GPU hardware architectures, processing pipelines,the concept and procedure for GPGPU computations, and the OpenGL shading la nguage arediscussed. The stream operations such as map and reduction are reviewed, and a new texturereduction algorithm not requiring the texture size be the order of 2 is presented. The datastructure, matrix-matrix multiplication, and matrix-vector multiplication for dense matrixoperations are studied. The Gauss elimina tion method and conjugate gradient method forsolving linear equations are implemented by the GPU. The sparse matrix-vector multiplicationis also implemented by the GPU.In this dissertation, the GPU is used to compute the following structural computations:①Structural dynamic response. The first natural frequency and all natural frequencies areobtained by the power method and the QR method, respectively. The GPU is used toaccelera te the Wilson-θmethod and Newmark method for computing the structural dynamicresponse.②Large scale finite element method computations. The incomplete Cholesk ydecomposition conjugate gradient method on the GPU is used to solve the larger scale sparsefinite element method equations.③Meshless method computations. The GPU is used toaccelera te the element free Galerkin method, which is used to compute the linear elasticproblems, elastic-plastic problems, and geometrica l nonlinear problems.④Linear molecularstructural mecha nics approach computations. This algorithm is used to analyze changes for theYoung's moduli while the dia meters of the carbon nanotubes increasing. The tension of thecarbon nanotubes whose degree of freedom are over 100,000 are computed, and the runningtimes on the GPU and on the CPU are compared.⑤Nonlinear molecular structuralmecha nics approach computations . The theorem and computationa l procedure for thenonlinear molecular mecha nics structural mecha nics approach are studied. The nonlinear formula of the carbon atom bond force for stretching, bending and torsion are deduced. Theincrement Newton-Raphson method for solving the nonlinear molecular structural mecha nicsapproach is given, and the GPU implementation for nonlinear molecular structural mecha nicsapproach is also given. These algorithms are used to analyze the carbon nanotubes'nonlinearstretching and torsiona l responses, and the running times on the GPU algorithms and on theCPU algorithms are compared. These computationa l results show that the computations on theGPU have good computationa l accuracy, while the degree of freedom increasing, the runningtimes on the GPU are less tha n those on the CPU, proving that the GPU can accelera te thecomputations for med ium and large structures.Although GPGPU computations are being applied in ma ny fields, the computations on theGPU have such deficiencies as only single precision real being provided, the GPU programsbeing complex and trivia l, data transfer between the GPU and the CPU being deficient, etc.Further research is necessary in the following: The GPU is used to accelera te moleculardynamics computations, and employ this algorithm to analyze carbon nanotubes; The GPU isused to search the nodes within the influence doma in in meshless method; As a storageelement, the GPU is used to store the blocks of the stiffness matrix for large scale finiteelement computations; etc.