Three-Dimensional Weak-Form DRGMRES-NUFFT for Volume Integral Equations

2006 ◽  
Author(s):  
P.L. Rui ◽  
S.S. Li ◽  
R.S. Chen
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Weak Form ◽  
Volume Integral

scholarly journals Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations

2020 ◽  
Vol 50 (1) ◽  
Author(s):  
Maciej Kraszewski ◽  
Jerzy Pluciński
Keyword(s):  
Monte Carlo ◽  
Light Scattering ◽  
Integral Equations ◽  
Three Dimensional ◽  
Monte Carlo Algorithm ◽  
Refractive Indices ◽  
Algebraic Equations ◽  
Volume Integral ◽  
Scattering Process ◽  
Convergence Properties

The light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present the implementation of this algorithm for one- and three-dimensional light scattering computations and discuss its applicability in this field. We show that the Monte Carlo algorithm can provide valid and accurate results but, due to its convergence properties, it might be difficult to apply for problems with large volumes or refractive indices of scattering objects.

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