CAJ | 학술논문

对Jacobi-Davidson（J-D）算法进行了改进和并行计算研究。通过添加谱变换、收缩和重启动等策略将J-D算法改造成了适应大规模模态分析的算法。利用改进后的算法和各种数值求解软件包，建立了一套基于PANDA框架的模态分析并行求解体系。基于该求解体系和并行机群，开展了某工程结构大规模模态分析并行可扩展性研究，测试规模从数十万自由度一直达到千万自由度，并行CPU核数达到128个；研究了改进后的J-D算法内层迭代步数、重启动向量个数等控制参数对外层迭代收敛速度的影响；获取了不同规模并行计算的加速比。研究结果表明，改进后的J-D算法完全适应千万自由度规模以上的模态分析，内存占用与规模之间呈线性增长趋势，在1025万自由度规模模态分析仅占用39．4 GB内存；同时该算法具有优异的并行可扩展性，在128个CPU测试核内接近线性加速，并且测试规模越大，曲线越接近理想加速曲线，1025万自由度规模在128核的并行效率达到88．1％。
대Jacobi-Davidson（J-D）산법진행료개진화병행계산연구。통과첨가보변환、수축화중계동등책략장J-D산법개조성료괄응대규모모태분석적산법。이용개진후적산법화각충수치구해연건포，건립료일투기우PANDA광가적모태분석병행구해체계。기우해구해체계화병행궤군，개전료모공정결구대규모모태분석병행가확전성연구，측시규모종수십만자유도일직체도천만자유도，병행CPU핵수체도128개；연구료개진후적J-D산법내층질대보수、중계동향량개수등공제삼수대외층질대수렴속도적영향；획취료불동규모병행계산적가속비。연구결과표명，개진후적J-D산법완전괄응천만자유도규모이상적모태분석，내존점용여규모지간정선성증장추세，재1025만자유도규모모태분석부점용39．4 GB내존；동시해산법구유우이적병행가확전성，재128개CPU측시핵내접근선성가속，병차측시규모월대，곡선월접근이상가속곡선，1025만자유도규모재128핵적병행효솔체도88．1％。
Some improvements and parallel computing studies were carried out about the Jacobi-Davidson(J-D) method.Some strategies,such as the spectral transformation technique,restart and deflation techniques,were integrated with the J-D method to make it suitable for large-scale modal analysis.A parallel modal analysis system based on PANDA framework was created using the improved J-D algorithm and various numerical software packages.Utilizing the analysis system and parallel computers,the parallel scalability of the J-D algorithm was studied via numbers of tests on an engineering structure.The maximum computing scale is over 10 million degrees of freedom,and the maximum number of parallel CPU processors attains 128.The influences of inner iteration steps and number of restarted vectors on the convergence velocity of outer iterations were studied,and the speedup curves for different scales were obtained.The results show that the improved J-D method is competent for the large-scale modal analysis,the memory cost increases linearly with the computing scale and only 39.4 GB of memory is needed for the modal analysis of 10.25 million scale. Also,the improved J-D method takes on an excellent parallel scalability that the speedup curves are almost linear within 128 testing processors and the curve is gradually close to the ideal speedup one as the computing scale is accreting.The parallel efficiency of 10.25 million scale with 128 processors attains 88.1 %.