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math.PR2024★ 4 cited
A Stochastic Calculus Approach to Boltzmann Transport
J. Darby Smith, Rich Lehoucq, Brian Franke
Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contri…
math.NA2024
Optimal accuracy for linear sets of equations with the graph Laplacian
Richard B. Lehoucq, Michael Weylandt, Jonathan W. Berry
We show that certain Graph Laplacian linear sets of equations exhibit optimal accuracy, guaranteeing that the relative error is no larger than the norm of the relative residual and…