Spherical Harmmonic Transform Rapid Expaansion Algorithm Baseed On GPU And Application In Molecular Simulation

With the rapid development of Graphics Processing Unit(GPU),now,the theorycomputing capacity and memory bandwidth of GPU are much better than of theCPU.Comparing with the realization of clusters and supercomputers,the large-scaledata-intensive computing tasks,which are completed by GPU as a coprocessor ofCPU,have high performance/price ratio.Programmers through CUDA parallelprogramming environment can use GPU parallel computing,and do not need to learncomplex graphics APIs.The MPI+CUDA hybrid programming through twogranularity of threads and processes under the CPUs and GPUs computingenvironment to complete the parallel programming.Spherical harmonic transform as aimportant method to describe sphere or spheroid， is implemented in manydomains,such as molecular dynamics, astronomy, fluid mechanics, thermodynamics,and computer graphics.When spherical harmonic transform used to describe of thecomplex object,what kind of expansion algorithm to get the spherical harmonictransform coefficient directly affects the accuracy of the settlement results.In thisthesisi, spherical harmonic transform rapid expansion algorithm based on GPU, canaccelerate the molecular shape similarity computing speed, have important theoreticalsignificance and practical significance.Spherical harmonic transform rapid expansion algorithm,consisting of FourierTransform and Legendre Transform.Discrete Fourier transform using the divide andconquer method and butterfly computation reduces the time complexity and spacecomplexity.The general Legendre transformation using the famous three recurrenceformula for arbitrary order spherical harmonic coefficient, for the assessment of thediscrete points more spherical transformation, the efficiency is unsatisfactory.In thispaper, through linear transformation converts the original Chebyshev valuation withthe order of the polynomial approximation form, using spherical harmonic functionsampling point symmetry reduce amount of calculation.In this thesisi, Spherical harmonic transform rapid expansion algorithm based onGPU and its application in molecular simulation research, the main contents aremainly as follows:1.Studied parallel computing theory and technology, including CUDA parallelprogramming model and CUDA+MPI parallel programming model and themathematical basis of spherical harmonic transform rapid expansion algorithm; 2.Using CUBS, FFTW for CPU library function, implement serial sphericalharmonic transform expansion algorithm;3. Implement CUDA parallel program for spherical harmonic transform rapidexpansion algorithm, when the expansion order of spherical harmonic transformL=1024, the parallel algorithm accelerated ratio reached9.72. Implement CUDA+MPI parallel program for spherical harmonic transform rapid expansion algorithm,when the expansion order of spherical harmonic transform L=1024, the parallelalgorithm accelerated ratio reached14.66. The results show that use GPU to achievelarge-scale data-intensive computing tasks has a good performance.4.Using spherical harmonic function as a molecular space structure, according todata by the GPU spherical harmonic transform rapid algorithm to accelerate thespherical harmonic coefficient calculated molecular space structure characteristicvector, can shorten the time of the compare their similarity.