scholarly journals Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations

2020 ◽  
Vol 50 (1) ◽  
Author(s):  
Maciej Kraszewski ◽  
Jerzy Pluciński
Keyword(s):  
Integral Equation ◽  
Monte Carlo ◽  
Light Scattering ◽  
Numerical Methods ◽  
Dipole Approximation ◽  
Discrete Dipole Approximation ◽  
Monte Carlo Algorithm ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Large Particles

Various numerical methods were proposed for analysis of the light scattering phenomenon. An important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation. Discrete dipole approximation uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo algorithm as one of them was proposed. In this research, we analyze the application of the Monte Carlo algorithm for two cases: the light scattering by large particles and by random conglomerates of small particles. We show that if proper preconditioning of the numerical problem is applied, the Monte Carlo algorithm can solve the underlying systems of linear equations. We also show that the efficiency of the Monte Carlo algorithm can be increased by reusing performed computations for various incident electromagnetic waves and the applicability of the Monte Carlo algorithm depends on the particular use case. It is unlikely to be used in the case of light scattering by the large particles due to computational times inferior comparing with the other numerical methods but may become useful in the case of light scattering by the random conglomerates of small scattering particles.

scholarly journals Accuracy of internal fields in volume integral equation simulations of light scattering

1998 ◽  
Vol 37 (36) ◽  
pp. 8482 ◽  
Author(s):  
Alfons Hoekstra ◽  
Jussi Rahola ◽  
Peter Sloot
Keyword(s):  
Integral Equation ◽  
Light Scattering ◽  
Volume Integral ◽  
Volume Integral Equation

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.

The Numerical Methods of Peridynamics Theory Used in Failure Analysis of Materials

2014 ◽  
Vol 1030-1032 ◽  
pp. 223-227
Author(s):  
Lin Fan ◽  
Song Rong Qian ◽  
Teng Fei Ma
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Numerical Integration ◽  
Integration Method ◽  
Equation Of Motion ◽  
Numerical Integration Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Method Of Molecular Dynamics ◽  
Classic Theory

In order to analysis the force situation of the material which is discontinuity,we can used the new theory called peridynamics to slove it.Peridynamics theory is a new method of molecular dynamics that develops very quickly.Peridynamics theory used the volume integral equation to constructed the model,used the volume integral equation to calculated the PD force in the horizon.So It doesn’t need to assumed the material’s continuity which must assumed that use partial differential equation to formulates the equation of motion. Destruction and the expend of crack which have been included in the peridynamics’ equation of motion.Do not need other additional conditions.In this paper,we introduce the peridynamics theory modeling method and introduce the relations between peridynamics and classic theory of mechanics.We also introduce the numerical integration method of peridynamics.Finally implementation the numerical integration in prototype microelastic brittle material.Through these work to show the advantage of peridynamics to analysis the force situation of the material.

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