On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods
Authors:
Article info
2018-02-10
2018-12-06
45 - 56
Keywords
- Multigrid iterations.
- Heat conduction
- Fredholm integral equation
- Boundary element method
Abstract
In this work we consider the boundary integral equation describing the steady state heat conduction taking place in three dimensional enclosure geometries. For the numerical realization of the Fredholm integral equation, we use the boundary element method based on the Galerkin weighted residuals method. Consequently, converting the original integral equation into a set of algebraic equations. We apply the multigrid iterations to solve the system of linear equations. To demonstrate the efficiency of this iterative scheme, we construct numerical example.
Qatanani, N., & Sa’adAldin, A. (2019). On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods. An-Najah University Journal for Research - A (Natural Sciences), 33(1), 45–56. https://doi.org/10.35552/anujr.a.33.1.1614
[1]N. Qatanani and A. Sa’adAldin, “On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods,” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, pp. 45–56, Feb. 2019, doi: 10.35552/anujr.a.33.1.1614.
Qatanani, Naji, and AbdelLatif Sa’adAldin. “On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods.” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, Feb. 2019, pp. 45–56. Crossref, https://doi.org/10.35552/anujr.a.33.1.1614.
1.Qatanani N, Sa’adAldin A. On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2019 Feb;33(1):45–56. Available from: http://dx.doi.org/10.35552/anujr.a.33.1.1614
Qatanani, Naji, and AbdelLatif Sa’adAldin. “On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods.” An-Najah University Journal for Research - A (Natural Sciences) 33, no. 1 (February 2019): 45–56. https://doi.org/10.35552/anujr.a.33.1.1614.
المعالجة العددية لمشكلة التوصيل الحراري بواسطة طريقة العناصر الحدية والطرق متعددة المراحل
المؤلفون:
معلومات المقال
2018-02-10
2018-12-06
45 - 56
الكلمات الإفتتاحية
- Multigrid iterations.
- Heat conduction
- Fredholm integral equation
- Boundary element method
الملخص
في هذا العمل، نعتبر المعادلة التكاملية الحدودية الي تصف التوصيل الحراري الثابت للدولة الذي يحدث في هندسيات الضميمة ثلاثية الأبعاد. للتحقيق العددي لمعادلة فريدهولم التكاملية، نستخدم طريقة العناصر الحدودية على أساس طريقة المتبقيات المرجحة لغالركن، وبالتالي، تحويل المعادلة التكاملية الأصلية إلى مجموعة من المعادلات الجبرية. نطبق التكرار المتعدد لحل نظام المعادلات الخطية. لشرح كفاءة هذا المخطط التكراري، نبني مثالاً عددياً.
Qatanani, N., & Sa’adAldin, A. (2019). On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods. An-Najah University Journal for Research - A (Natural Sciences), 33(1), 45–56. https://doi.org/10.35552/anujr.a.33.1.1614
[1]N. Qatanani and A. Sa’adAldin, “On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods,” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, pp. 45–56, Feb. 2019, doi: 10.35552/anujr.a.33.1.1614.
Qatanani, Naji, and AbdelLatif Sa’adAldin. “On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods.” An-Najah University Journal for Research - A (Natural Sciences), vol. 33, no. 1, Feb. 2019, pp. 45–56. Crossref, https://doi.org/10.35552/anujr.a.33.1.1614.
1.Qatanani N, Sa’adAldin A. On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods. An-Najah University Journal for Research - A (Natural Sciences) [Internet]. 2019 Feb;33(1):45–56. Available from: http://dx.doi.org/10.35552/anujr.a.33.1.1614
Qatanani, Naji, and AbdelLatif Sa’adAldin. “On the Numerical Treatment of Heat Conduction Problem by Boundary Element and Multigrid Methods.” An-Najah University Journal for Research - A (Natural Sciences) 33, no. 1 (February 2019): 45–56. https://doi.org/10.35552/anujr.a.33.1.1614.
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