Simulation of the oxygen distribution in a tumor tissue using residual algorithms
Journal Title: Bulletin of Computational Applied Mathematics (Bull CompAMa) - Year 2015, Vol 3, Issue 1
Abstract
In this paper the use of recent residual algorithms for the simulation of the oxygen distribution in a tumor tissue in 2-D is proposed. The oxygen distribution in a tumor is considered a reaction-diffusion problem in steady state, whose mathematical model is a nonlinear partial differential equation, which is numerically solved using the traditional methods for systems of nonlinear equations (Newton's method, Broyden method, inexact Newton methods, etc.). Unlike of these traditional methods that require the use of derivatives and a large memory storage capacity, the proposed residual algorithms are derivative-free methods with low memory storage. The preliminary numerical results indicate that the proposed methods allows efficiently determine the distribution of oxygen in a tumor tissue to synthetic problems.
Authors and Affiliations
William La Cruz
Keywords
Related Articles
- EP ID EP240524
- DOI -
- Views 116
- Downloads 0
Some Convergence Strategies for the Alternating Generalized Projection Method
In this paper we extend the application of the alternating projection algorithm to solve the problem of finding a point in the intersection of $n$ sets ($n\geq2$), which are not all of them convex sets. Here we term such...
Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems
We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new prec...
A deterministic optimization approach for solving the rainfall disaggregation problem
One of the main problems in hydrology is the time scale of the historical rainfall data, available from many meteorological data bases. Most of the rainfall data is given at a time scale coarser than the one needed for...
Hole-filling techniques by using minimal energy surfaces
In the last few years, several techniques to fill holes of a given surface by means of minimal energy surfaces have been proposed. In all cases, the filling patches are obtained by minimizing an `energy functional' defin...
Sparse approximations of matrix functions via numerical integration of ODEs
We consider the numerical computation of matrix functions f(x) via matrix ODE integration. The solution is modeled as an asymptotic steady state of a proper differential system. The framework we propose, allows to define...