面向异构架构的混合精度有限元算法及其CUDA实现

Mixed Precision Finite Element Algorithm on Heterogeneous Architecture

长期以来,单精度似乎与科学计算无缘,然而从体系结构看,混合精度计算可以充分发挥向量部件、GPGPU设备的单精度性能,提供更高的效能,如降低通讯带宽要求、提高数据传输和通讯效率等。混合精度显格式有限元算法,结合材料强非线性多尺度有限元程序msFEM,实现了GPGPU上的有效加速。实验结果表明:混合精度显格式有限元程序实现了90%以上的计算通过单精度完成,其计算结果与全部使用双精度的结果相一致。该算法可以使得在不支持双精度格式的加速卡上实现科学计算功能。在支持双精度浮点格式的GPU上,混合精度算法与全部采用双精度计算相比其加速效果提高了1.6～1.7倍。

For a long time,single precision has been giving away to double precision in scientific computing.However,on computer architectures,mixed-precision computing,can take full advantages of excellent computing compatibilities of vector components,GPGPU,offering merits such as reducing communication bandwidth requirements,improving data movement efficiency etc.A mixed-precision explicit finite-element algorithm was proposed and implemented on nVidia GPU for strongly nonlinear multi-scale material simulation.The developed mixed-precision finite-element method gives the same results as that of the fully double-precision calculation,while keeping a 90% portion of finite element calculations to be done by single precision float calculation.As a result,on the device that does not support native double precision float format,the mixed-precision algorithm makes it possible to fulfill double precision finite element simulation,while on the device that supports the native double precision,the mixed-precision algorithm is 1.6～1.7 times faster than the full double precision calculation.