基于GPU的隐式算法与方案研究

The Research of the Implicit Algorithm and Program Based on the GPU

图形处理单元（GPU）可以将桌面计算机的计算速度提高1～2个数量级，发展相关的隐式算法非常重要。本研究根据GPU的硬件特点，选择了DP—LUR隐式方法，并对此进行了进一步的改进。根据GPU算法低内存需求，首先对DP—LUR方法右端项相关矩阵运算进行改写，将其变化为具有推广价值的标量形式。这一改进与原始方法完全等价，但形式极为简洁，节省了大量的内存存储与读写需求。随后，进一步将左端项矩阵对角化，从而对内存存储与读写的需求进一步降低，同时降低了单步迭代计算量，但也同时降低了收敛速度，总计算量比前一种方法增加了约20％。以上两种改进相互独立，可以根据需要单独或联合选取。

The computation speed of desktop computer can be accelerated 10~100 times by Graphic Processing Unit （GPU）. Therefore, it is very important to develop corresponding implicit algorithm. According to the hardware characteristic of GPU, the DP-LUR implicit method is chosen and improved. According to the requirement of low memory, the matrix operation of the right term is rewritten as scalar form which can be extended. This improvement does not change the nature of origin method, but has very concise form and save many memory storage, read and written requirement. Further, the left term is changed diagonally. It decreases the memory storage, read and written requirement further. It also decreases the computation time for the one iteration, however, the totally computation time increases about 20%, because the convergence speed is decreased simultaneously. Above two improvements are independent of each other, and can be individually or jointly adopted according to requirement.