Finite element method for spatial fractional PDEs on 3-D domains

Finite element method, a good candidate to solve fractional partial differential equations (FPDEs), has been used to solve temporal FPDEs or spatial FPDEs in 1-D or 2-D. However, due to its non-local property, it is very hard to form the stiffness matrix in 3-D cases. Thus, we present an easy way to assemble it. During searching the integral path, a ray-simplex intersection algorithm is suggested to avoid aimless searching. Using our method, steady spatial FPDEs with constant/variable coefficients and fractional reaction-diffusion problems all can be solved with high efficiency, as illustrated by some numerical examples.