Robust Alternating Direction Implicit Solver in Quantized Tensor Formats for a Three-Dimensional Elliptic PDE

2021 ◽  
Vol 43 (2) ◽  
pp. A800-A827
Author(s):  
M. Rakhuba
Keyword(s):  
Three Dimensional ◽  
Elliptic Pde ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Implicit Solver

An Error-Reduced ADI-FDTD Algorithm in Debye Media

2013 ◽  
Vol 765-767 ◽  
pp. 567-571
Author(s):  
Hui Fu ◽  
Chuan Wen Zhu ◽  
Gang Guo ◽  
Quan Min Wang
Keyword(s):  
Large Time ◽  
Fdtd Method ◽  
Three Dimensional ◽  
Alternating Direction Implicit ◽  
Truncation Errors ◽  
Computation Efficiency ◽  
Alternating Direction ◽  
Implicit Finite Difference ◽  
Fdtd Methods ◽  
Difference Time

The alternating direction implicit finite-difference time-domain (ADI-FDTD) method is an unconditionally stable numerical scheme, being proposed to remove stability limitations in conventional FDTD methods. Though the computation efficiency has been improved by ADI-FDTD, significant errors have been observed at large time steps. By compensating truncation errors, a low error ADI-FDTD method in Debye media is proposed based the ER(error reduced)-ADI-FDTD, complete three dimensional equations are derived. Simulation results are anlalyzed and compared with existing methods.

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