Monte-Carlo and sensitivity transport models for domain deformation

Abstract

We address the question of evaluating shape derivatives of objective functions for radiative-transfer engineering involving semi-transparent media. After recalling the standard Monte-Carlo approach to sensitivity estimation and its current limitations, a new method is presented for the specific case of geometrical sensitivities. This method is then tested on configurations with multiple-scattering and absorbing (nonemitting) semi-transparent medium. A new geometrical sensitivity algorithm is presented with full details in order to extend, on several examples, its implementation in complex geometries.

The Past and Future of the Monte Carlo Method in Thermal Radiation Transfer

“…Today, Monte Carlo is used to carry out simulations of scope and complexity that surely could not have been imagined by Ulam, von Neumann, Metropolis, and Fermi nearly 80 years ago. Recent examples include radiative loading on clouds, which is important for climate change modeling [118][119][120], radiative transfer within complex heterogeneous [121,122] and graded media [108,[123][124][125][126][127], polarization [128][129][130][131], shape optimization [69][70][71], computer graphics rendering [118], large scale systems [132,133], manufacturing [134][135][136][137], combined-mode problems [138][139][140][141][142][143][144], and others .…”

“…The capabilities of MC have expanded to include sensitivity analysis and nonlinear problems [38,71], by taking a more fundamental viewpoint of Monte Carlo as a tool for solving integrals. For example, Roger et al [69] showed that domain sensitivities may be obtained by direct differentiation of the integrals governing radiative transport between surfaces separated by transparent media.…”

“…For example, Roger et al [69] showed that domain sensitivities may be obtained by direct differentiation of the integrals governing radiative transport between surfaces separated by transparent media. This approach was extended to participating media [71,176] by virtue of the null-collision technique, which amounts to reformulating the RTE as a Fredholm integral equation.…”

“…Above all, obtaining a statistically robust estimate routinely involves carrying out millions, and often billions, of trials, which can be a time-consuming process. The statistical error that contaminates the estimates can also introduce numerical instabilities, e.g., when calculating the radiant source term in mixed mode heat transfer problems [68] and determining sensitivities during shape optimization [69][70][71]. However, recent developments focused on reducing the variance of the MC estimates [38,[72][73][74][75][76][77][78][79][80][81][82][83], combined with radical improvements in computing power (e.g., multithreaded cores, GPUs) are dissolving these barriers.…”

Coupling radiative, conductive and convective heat-transfers in a single Monte Carlo algorithm: A general theoretical framework for linear situations

“…computing spatial gradients or parametric and geometric sensitivities; solutions are starting to emerge from a better understanding of the information carried by thermal paths that is available for further quantitative analysis [ 11 , 123 – 126 ];…”