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Register a new userConvergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy
تقارب التقدير الذراعي المنفصل. II. تقنية استخدام التحسين لزيادة الدقة
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نقترح تقنية اكسترابوليشن تسمح بتحسين دقة الحسابات التقريب الثنائي المقطع. تم دراسة أداء هذه التقنية على أساس تجارب كبيرة لخمسة حالات اختبار باستخدام العديد من التقطيعات المختلفة. كانت جودة الاكسترابوليشن يتحسن مع التقطيع المحسن بشكل كبير خاصة للجسيمات المشكلة بشكل كوبي. تم إثبات تخفيض فائدة مرتفعة من الخطأ. كما نقترح تقديرات لخطأ الاكسترابوليشن الذي تم إثباته أنه موثوق به. وأخيرا نقترح طريقة بسيطة لفصل خطأ الشكل والتقطيع وذلك باستخدام حالة اختبار واحدة.
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different discretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case.
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We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in th
e range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their consequences for convergence.
We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a
general framework based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light scattering simulation is shown and possible future developments are discussed.
In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available DDA compu
ter program that processes the large number of dipoles required for such simulations. Numerical simulations of light scattering by spheres with size parameters x up to 160 and 40 for refractive index m=1.05 and 2 respectively are presented and compared with exact results of the Mie theory. Errors of both integral and angle-resolved scattering quantities generally increase with m and show no systematic dependence on x. Computational times increase steeply with both x and m, reaching values of more than 2 weeks on a cluster of 64 processors. The main distinctive feature of the computer program is the ability to parallelize a single DDA simulation over a cluster of computers, which allows it to simulate light scattering by very large particles, like the ones that are considered in this manuscript. Current limitations and possible ways for improvement are discussed.
We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T-matrix for modeling arbitrarily shaped micro-sized objects. The emph{T}-matrix elements are calculated using point matching between fields calculated using vector spherical wave functions and DDA. When applied to microrotors, their discrete rotational and mirror symmetries can be exploited to reduce memory usage and calculation time by orders of magnitude; a number of optimization methods can be employed based on the knowledge of the relationship between the azimuthal mode and phase at each discrete rotational point, and mode redundancy from Floquets theorem. A reduced-mode T-matrix can also be calculated if the illumination conditions are known.
The accuracy of calculation of spectral line shapes in one-dimensional approximation is studied analytically in several limiting cases for arbitrary collision kernel and numerically in the rigid spheres model. It is shown that the deviation of the line profile is maximal in the center of the line in case of large perturber mass and intermediate values of collision frequency. For moderate masses of buffer molecules the error of one-dimensional approximation is found not to exceed 5%.
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