Diffraction nonlocal boundary condition (BC) is one kind of the transparent boundary condition which is used in the finite-difference (FD) parabolic equation (PE). The greatest advantage of the diffraction nonlocal boundary condition is that it can absorb the wave completely by using one layer of grid. However, the speed of computation is low because of the time-consuming spatial convolution integrals. To solve this problem, we introduce the recursive convolution (RC) with vector fitting (VF) method to accelerate the computational speed. Through combining the diffraction nonlocal boundary with RC, we achieve the improved diffraction nonlocal BC. Then we propose a wide-angle three-dimensional parabolic equation (WA-3DPE) decomposition algorithm in which the improved diffraction nonlocal BC is applied and we utilize it to predict the wave propagation problems in the complex environment. Numeric computation and measurement results demonstrate the computational accuracy and speed of the WA-3DPE decomposition model with the improved diffraction nonlocal BC.
Global blow-up for a localized nonlinear parabolic equation with a nonlocal boundary condition
