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AFIT researchers have developed a new approach to solving Discrete Ordinates equations, which approximate the linear Boltzmann Transport Equation (BTE). The usual approach is von Neumann iteration on the scattering source, which requires repeated sweeps through the spatial-angular grid. Acceptable convergence requires complicated and expensive acceleration schemes. The new approach, Partial-Current Transport (PCT) with Adaptive Distribution Iteration, eliminates scattering source iteration through matrix inversions and a reduced-size global linear algebra problem. It creates the needed matrices directly from the standard spatial quadratures used in the sweeping. Positivity, linearity, and (higher-than-first-order) accuracy are the key desirable qualities with all Discrete Ordinates methods, but all three, according to Lathrop [8], cannot be achieved simultaneously. If a high order accurate, linear method is used, it can produce negative fluxes. Non-linear methods have been developed that are high-order accurate and positive, but these methods are not widely accepted because the BTE is itself a linear equation.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
