This study proposes a hybrid collocation approach for simulating heat conduction problems in anisotropic functionally graded materials over extended time intervals. In this approach, the Krylov deferred correction (KDC) scheme is employed for the temporal discretization of dynamic problems, featuring a novel numerical implementation designed to ensure the precise satisfaction of boundary conditions. The localized radial basis function (LRBF) collocation method is modified and utilized to solve the resulting boundary value problems. A new radial basis function is developed and combined with an optimization strategy for the distribution of source points to enhance the performance of the LRBF scheme. This method synergizes the KDC technique, which supports large time step sizes, with the LRBF collocation method, characterized by its truly meshless nature, to address dynamic problems over long durations. Additionally, the coefficient matrix produced by the LRBF method is sparse and depends solely on the spatial distances between collocation points and source points, which is advantageous for long-term simulations. Numerical simulations spanning thousands of time steps demonstrate the accuracy, stability, and convergence of the hybrid approach. The developed numerical framework shows significant improvements over existing methods, particularly in handling dynamic problems with substantial temperature variations.
机构:Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, Technological Institute, Northwestern University, Evanston, Illinois
BELYTSCHKO, T
LU, YY
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机构:Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, Technological Institute, Northwestern University, Evanston, Illinois
LU, YY
GU, L
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机构:Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, Technological Institute, Northwestern University, Evanston, Illinois
机构:
Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
Univ Southern Mississippi, Sch Math & Nat Sci, Hattiesburg, MS 39406 USAUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
Chen, C. S.
Karageorghis, Andreas
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Univ Cyprus, Dept Math & Stat, POB 20537, CY-1678 Nicosia, CyprusUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
Karageorghis, Andreas
Dou, Fangfang
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Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
机构:
Xi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Ecole Polytech Fed Lausanne, Chair Computat Math & Simulat Sci, CH-1015 Lausanne, SwitzerlandXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Chen, Wenqian
Wang, Qian
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Ecole Polytech Fed Lausanne, Chair Computat Math & Simulat Sci, CH-1015 Lausanne, SwitzerlandXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Wang, Qian
Hesthaven, Jan S.
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Ecole Polytech Fed Lausanne, Chair Computat Math & Simulat Sci, CH-1015 Lausanne, SwitzerlandXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Hesthaven, Jan S.
Zhang, Chuhua
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h-index: 0
机构:
Xi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R ChinaXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
机构:Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, Technological Institute, Northwestern University, Evanston, Illinois
BELYTSCHKO, T
LU, YY
论文数: 0引用数: 0
h-index: 0
机构:Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, Technological Institute, Northwestern University, Evanston, Illinois
LU, YY
GU, L
论文数: 0引用数: 0
h-index: 0
机构:Department of Civil Engineering, Robert R. McCormick School of Engineering and Applied Science, Technological Institute, Northwestern University, Evanston, Illinois
机构:
Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
Univ Southern Mississippi, Sch Math & Nat Sci, Hattiesburg, MS 39406 USAUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
Chen, C. S.
Karageorghis, Andreas
论文数: 0引用数: 0
h-index: 0
机构:
Univ Cyprus, Dept Math & Stat, POB 20537, CY-1678 Nicosia, CyprusUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
Karageorghis, Andreas
Dou, Fangfang
论文数: 0引用数: 0
h-index: 0
机构:
Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R ChinaUniv Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China
机构:
Xi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Ecole Polytech Fed Lausanne, Chair Computat Math & Simulat Sci, CH-1015 Lausanne, SwitzerlandXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Chen, Wenqian
Wang, Qian
论文数: 0引用数: 0
h-index: 0
机构:
Ecole Polytech Fed Lausanne, Chair Computat Math & Simulat Sci, CH-1015 Lausanne, SwitzerlandXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Wang, Qian
Hesthaven, Jan S.
论文数: 0引用数: 0
h-index: 0
机构:
Ecole Polytech Fed Lausanne, Chair Computat Math & Simulat Sci, CH-1015 Lausanne, SwitzerlandXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China
Hesthaven, Jan S.
Zhang, Chuhua
论文数: 0引用数: 0
h-index: 0
机构:
Xi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R ChinaXi An Jiao Tong Univ, Sch Energy & Power Engn, Dept Fluid Machinery & Engn, Xian, Shaanxi, Peoples R China