آمار
| تعداد نشریات | 45 |
| تعداد شمارهها | 1,499 |
| تعداد مقالات | 18,319 |
| تعداد مشاهده مقاله | 59,470,165 |
| تعداد دریافت فایل اصل مقاله | 20,799,959 |
Newton-multigrid method for nonlinear silicon problem with relaxing boundary conditions | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 فروردین 1405 اصل مقاله (1.25 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.67988.3259 | ||
| نویسندگان | ||
| Adriano Rodrigues de Melo* 1؛ Marcio Augusto Villela Pinto2؛ Sebastião Romero Franco3؛ Priscila Dombrovski Zen4 | ||
| 1Catarinense Federal Institute, BR-280, Araquari, 89245-000, Santa Catarina, Brazil. | ||
| 2Department of Mechanical Engineering, Federal University of Paran\'{a}, Polytechnic Center, Curitiba, 81530-000, Paran\'{a}, Brazil. | ||
| 3Department of Mathematics, State University of the Central West, Irati, 84505-677, Paran\'{a}, Brazil. | ||
| 4Graduate Program in Numerical Methods in Engineering, Federal University of Paran\'{a}, Polytechnic Center, Curitiba, 81530-000, Paran\'{a}, Brazil. | ||
| چکیده | ||
| This paper introduces a Newton-multigrid (Newton-MG) method to efficiently solve a nonlinear heat transfer problem in a homogeneous silicon rod. The numerical model is constructed using the Finite Difference Method (FDM) with a Central Difference Scheme (CDS) for spatial discretization and the Crank-Nicolson method for temporal approximation. Newton's method is applied to linearize the discretized equations and a multigrid Correction Scheme (CS) is integrated to solve the resulting linear system. Computational experiments demonstrate that, regardless of the physical and numerical parameters, the apparent order of discretization error converges to its theoretical asymptotic order. Additionally, the Newton-MG method exhibits rapid convergence, requiring few linearization steps while achieving a favorable convergence factor. The efficiency gain relative to the singlegrid method increases with the degree of nonlinearity in the physical model. Our findings confirm that Newton-MG is a robust and computationally efficient alternative for nonlinear heat conduction problems. | ||
| کلیدواژهها | ||
| Convective heat transfer؛ Multigrid correction scheme؛ Semiconductor modeling؛ Time-stepping methods | ||
|
آمار تعداد مشاهده مقاله: 36 تعداد دریافت فایل اصل مقاله: 47 |
||