کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
519162 867642 2015 34 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions
ترجمه فارسی عنوان
یک روش گره مجازی دوم برای مشکلات بیضوی با رابط ها و دامنه های نامنظم در سه بعد
کلمات کلیدی
مشکلات رابط بیضوی، روش های جاسازی شده روش گره مجازی، روشهای متنوع، روش های چند گری
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی

We present a numerical method for the variable coefficient Poisson equation in three-dimensional irregular domains and with interfacial discontinuities. The discretization embeds the domain and interface into a uniform Cartesian grid augmented with virtual degrees of freedom to provide accurate treatment of jump and boundary conditions. The matrix associated with the discretization is symmetric positive definite and equal to the standard 7-point finite difference Poisson stencil away from embedded interfaces and boundaries. Numerical evidence suggests second order accuracy in the L∞-norm. Our approach improves the treatment of Dirichlet and jump constraints in the recent work of Bedrossian et al. [1] and introduces innovations necessary in three dimensions. Specifically, we construct new constraint-based Lagrange multiplier spaces that significantly improve the conditioning of the associated linear system of equations; we provide a method for cell-local polyhedral approximation to the zero isocontour surface of a level set needed for three-dimensional embedding; and we show that the new Lagrange multiplier spaces naturally lead to a class of easy-to-implement multigrid methods that achieve near optimal efficiency, as shown by numerical examples. For the specific case of a continuous Poisson coefficient in interface problems, we provide an expansive treatment of the construction of a particular solution that satisfies the value jump and flux jump constraints. As in [1], this is used in a discontinuity removal technique that yields the standard 7-point stencil across the interface and only requires a modification to the right-hand side of the linear system.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 231, Issue 4, 20 February 2012, Pages 2015–2048
نویسندگان
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