A Fast Finite Difference Method for Three-Dimensional Time-Dependent Space-Fractional Diffusion Equations with Fractional Derivative Boundary Conditions

By Meng Zhao, Hong Wang, Aijie Cheng. 2018

17 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. Lu Lu
2. G. Em Karniadakis
3. Guofei Pang

In Modeling and Simulation

1. G. Em Karniadakis
2. Lu Lu
3. Guofei Pang
4. Lexing Ying
5. Victor Minden
6. Zhiping Mao
7. Xuhui Meng

In Numerical Analysis

1. G. Em Karniadakis
2. Lexing Ying
3. Lu Lu
4. Guofei Pang
5. Victor Minden

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “In [36, 37, 38, 39], only the 3D extension of the Riesz space-fractional derivatives is considered, which differs from the directional fractional Laplacian of our interest; in [40], Riesz fractional Laplacian is first regularized by singularity subtraction and then approximated by using trapezoidal ”
• A Simple Solver for the Fractional Laplacian in Multiple Dimensions (2018, background): “[10] consider a multidimensional discretization and fast preconditioners based on multigrid, but their scheme uses the so-called coordinate fractional Laplacian that takes a tensor product of one-dimensional operators and is not equivalent to (1) (see also related finite-difference approaches with d”