English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We investigate integral formulations and fast algorithms for the steady-stateradiative transfer equation with isotropic and anisotropic scattering. When thescattering term is a smooth convolution on the unit sphere, a model reductionstep in the angular domain using the Fourier transformation in 2D and thespherical harmonic transformation in 3D significantly reduces the number ofdegrees of freedoms. The resulting Fourier coefficients or spherical harmoniccoefficients satisfy a Fredholm integral equation of the second kind. We studythe uniqueness of the equation and proved an a priori estimate. For ahomogeneous medium, the integral equation can be solved efficiently using theFFT and iterative methods. For an inhomogeneous medium, the recursiveskeletonization factorization method is applied instead. Numerical simulationsdemonstrate the efficiency of the proposed algorithms in both homogeneous andinhomogeneous cases and for both transport and diffusion regimes.

Fast algorithms for integral formulations of steady-state radiative transfer equation