TY - GEN
T1 - Relaxation schemes for the M1 model with space-dependent flux in radiotherapy
AU - Pichard, Teddy
AU - Frank, Martin
AU - Aregba-Driollet, Denise
AU - Brull, Stphane
AU - Dubroca, Bruno
PY - 2015/1/1
Y1 - 2015/1/1
N2 - Because of stability constraints, most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar. This problem emerges with the M\ system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities. Additionally, the flux term of the M1 system is non-linear, and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability. In this paper, we propose a numerical method that overcomes the stability constraint and preserves the realizability property. For this purpose, we relax the M1 system to obtain a linear flux term. Then we extend the stencil of the difference quotient to obtain stability. The scheme is applied to a radiotherapy dose calculation example.
AB - Because of stability constraints, most numerical schemes applied to hyperbolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar. This problem emerges with the M\ system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities. Additionally, the flux term of the M1 system is non-linear, and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability. In this paper, we propose a numerical method that overcomes the stability constraint and preserves the realizability property. For this purpose, we relax the M1 system to obtain a linear flux term. Then we extend the stencil of the difference quotient to obtain stability. The scheme is applied to a radiotherapy dose calculation example.
KW - Method of characteristics
KW - Moments models
KW - Radiotherapy
KW - Relaxation models
UR - https://www.scopus.com/pages/publications/84949521177
M3 - Conference contribution
AN - SCOPUS:84949521177
T3 - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015
SP - 547
EP - 558
BT - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015
PB - American Nuclear Society
T2 - Mathematics and Computations, Supercomputing in Nuclear Applications and Monte Carlo International Conference, M and C+SNA+MC 2015
Y2 - 19 April 2015 through 23 April 2015
ER -