Implicit Solvation Using a Generalized Finite-Difference Approach in CRYSTAL: Implementation and Results for Molecules, Polymers, and Surfaces

2018 ◽  
Vol 14 (11) ◽  
pp. 5969-5983 ◽  
Author(s):  
Frédéric Labat ◽  
Bartolomeo Civalleri ◽  
Roberto Dovesi
Keyword(s):  
Finite Difference ◽  
Implicit Solvation ◽  
Finite Difference Approach

scholarly journals COMPUTATION OF THE MODES OF ELLIPTIC WAVEGUIDES WITH A CURVILINEAR 2D FREQUENCY-DOMAIN FINITE-DIFFERENCE APPROACH

2012 ◽  
Vol 26 ◽  
pp. 69-84 ◽  
Author(s):  
Alessandro Fanti ◽  
Giuseppe Mazzarella ◽  
Giorgio Montisci ◽  
Giovanni Andrea Casula
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Finite Difference Approach

scholarly journals Curvilinear vector finite difference approach to the computation of waveguide modes

2012 ◽  
Vol 1 (1) ◽  
pp. 29 ◽  
Author(s):  
A. Fanti ◽  
G. Mazzarella ◽  
G. Montisci
Keyword(s):  
Finite Difference ◽  
Decomposition Method ◽  
Taylor Expansion ◽  
Waveguide Section ◽  
Elliptic Case ◽  
Waveguide Modes ◽  
Mode Function ◽  
Vector Mode ◽  
Spurious Modes ◽  
Finite Difference Approach

We describe here a Vector Finite Difference approach to the evaluation of waveguide eigenvalues and modes for rectangular, circular and elliptical waveguides. The FD is applied using a 2D cartesian, polar and elliptical grid in the waveguide section. A suitable Taylor expansion of the vector mode function allows to take exactly into account the boundary condition. To prevent the raising of spurious modes, our FD approximation results in a constrained eigenvalue problem, that we solve using a decomposition method. This approach has been evaluated comparing our results to the analytical modes of rectangular and circula rwaveguide, and to known data for the elliptic case.

scholarly journals Finite Difference Algorithm on Non-Uniform Meshes for Modeling 2D Magnetotelluric Responses

Algorithms ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 203
Author(s):  
Xiaozhong Tong ◽  
Yujun Guo ◽  
Wei Xie
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Analytical Solutions ◽  
Good Accuracy ◽  
Validity And Reliability ◽  
Homogeneous Half Space ◽  
1D Model ◽  
Relative Errors ◽  
Future Project ◽  
Finite Difference Approach

A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the calculation formula of this scheme from the boundary value problem of electric field and magnetic field, and compared finite-difference solutions with finite-element numerical results and analytical solutions of a 1D model. First, a homogeneous half-space model was tested and the finite-difference approach can provide very good accuracy for 2D magnetotelluric modeling. Then we compared them to the analytical solutions for the two-layered geo-electric model; the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased. To conclude, we compare our finite-difference simulation results with COMMEMI 2D-0 model with the finite-element solutions. Both results are in close agreement to each other. These comparisons can confirm the validity and reliability of our finite-difference algorithm. Moreover, a future project will extend the 2D structures to 3D, where non-uniform meshes should perform especially well.

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