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On the multigrid method in modeling tumor growth with estimation and reduction of discretization error | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 شهریور 1405 اصل مقاله (1.18 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.68119.3282 | ||
| نویسندگان | ||
| Jesika Maganin* 1؛ Marcio Augusto Villela Pinto1؛ Neyva Maria Lopes Romeiro2؛ Sebastião Romero Franco3 | ||
| 1Graduate Program in Numerical Methods in Engineering, Federal University of Paraná, Curitiba, Brazil. | ||
| 2Department of Mathematics, State University of Londrina, Londrina, Paraná, Brazil. | ||
| 3Department of Mathematics, State University of the Central West, Irati, Paraná, Brazil. | ||
| چکیده | ||
| In this work, we investigate the efficient solution of a two-dimensional model of avascular tumor growth, described by a transient system of four partial differential equations, two of which are nonlinear. The main contribution of this study lies in the strategic combination of the multigrid method with the standard Repeated Richardson Extrapolation (RRE) technique, aiming to reduce discretization error and enhance computational performance. The system was discretized using finite differences: central differences for the spatial terms and the Crank-Nicolson scheme for the temporal discretization. Linearization was performed via Taylor series expansion, and the resulting linear system was solved using the red-black Gauss-Seidel iterative method accelerated by multigrid. Code verification was initially carried out using a manufactured solution with Dirichlet boundary conditions, allowing accurate error analysis. Subsequently, a realistic setting was simulated, using an initial condition that characterizes tumor morphology. The results show that the combination of the multigrid method and the RRE technique significantly reduced computational time while maintaining a consistently low average convergence factor and producing highly accurate and reliable solutions, demonstrating the potential of the proposed multigrid-RRE approach for the accurate and efficient numerical simulation of avascular tumor growth models. | ||
| کلیدواژهها | ||
| Numerical simulation؛ Finite difference method؛ Biomathematics؛ Multigrid؛ Repetead Richardson Extrapolation | ||
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آمار تعداد مشاهده مقاله: 4 تعداد دریافت فایل اصل مقاله: 2 |
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