A parallel iterative solver for 3-D frequency-domain seismic wave modeling in viscoelastic anisotropic media

It is always challenging to solve a large sparse linear system in frequency-domain forward modelling in seismic full-waveform inversion. Moreover, in viscoelastic anisotropic media, because the number of moduli and nonzero elements in the matrix grows higher, the computational load is heavier than in viscoacoustic media. To solve this issue, parallel direct solvers (e.g., MUMPS) can be used, but the cost of computer resources is usually too expensive to afford. By contrast, iterative solvers require much fewer computer resources, but they usually have a slow convergence and difficulty in solving multiple sources. Therefore, we demonstrate a parallel iterative solver named P-PCG that enables us to deal with the multiple sources simultaneously but without greatly increasing memory cost. The linear system in our modelling has a dimension of 35.5 million and over 3.9 billion nonzero elements in the matrix. To accomplish this work, MUMPS takes 13.6 hours, 4407 gigabytes and 17 cores, whereas P-PCG only takes 6.3 hours, 64 gigabytes and 5 cores. Another multiple-source modelling shows that on our computer P-PCG can solve 15 sources simultaneously with acceptable speed and much less memory cost than MUMPS. Thus, the P-PCG is a good alternative solver when the computational resources are limited.