scholarly journals An efficient and high-order convergence mode solver for solving graphene and phosphorene-based waveguides

2021 ◽  
Vol 29 (2) ◽  
pp. 1147
Author(s):  
Chia-Chien Huang
Keyword(s):  
High Order ◽  
Order Convergence ◽  
High Order Convergence ◽  
Mode Solver

scholarly journals Variations on Hermite Methods for Wave Propagation

2017 ◽  
Vol 22 (2) ◽  
pp. 303-337 ◽  
Author(s):  
Arturo Vargas ◽  
Jesse Chan ◽  
Thomas Hagstrom ◽  
Timothy Warburton
Keyword(s):  
Wave Propagation ◽  
Time Evolution ◽  
Discontinuous Galerkin ◽  
Hermite Interpolation ◽  
High Order ◽  
New Method ◽  
Order Convergence ◽  
Hyperbolic Pdes ◽  
High Order Convergence ◽  
Dg Methods

AbstractHermite methods, as introduced by Goodrich et al. in [15], combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite method which do not involve time evolution on dual grids. Computational evidence is presented regarding stability, high order convergence, and dispersion/dissipation properties for each new method. Hermite methods may also be coupled to discontinuous Galerkin (DG) methods for additional geometric flexibility [4]. An example illustrates the simplification of this coupling for Hermite methods.

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