کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6929018 1449352 2018 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface
ترجمه فارسی عنوان
روش چند منظوره نقطه دلخواه اختلاف فوریه دوم برای مشکلات بیضوی با ضرایب منفرد بر روی یک رابط دلخواه
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 361, 15 May 2018, Pages 299-330
نویسندگان
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