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The complex variable interpolating moving least-squares method. (English) Zbl 1291.65138
Summary: In this paper, a new method for deriving the moving least-squares (MLS) approximation is presented first. Considering the unclear physical meaning of the functional in the existing complex variable moving least-squares (CVMLS) approximation, an improved CVMLS approximation is presented by constructing a new functional with an explicit physical meaning. Based on the improved CVMLS approximation, the complex variable interpolating moving least-squares (CVIMLS) method is presented, and the interpolating property of the corresponding shape function of the CVIMLS method is proved.

MSC:
65F30 Other matrix algorithms (MSC2010)
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[1] Bai, F.; Li, D.; Wang, J.; Cheng, Y., An improved complex variable element-free Galerkin (ICVEFG) method for two-dimensional elasticity problems, Chinese physics B, 21, 020204, (2012)
[2] Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P., Meshless method: an overview and recent developments, Computer methods in applied mechanics and engineering, 139, 3-47, (1996) · Zbl 0891.73075
[3] Belytschko, T.; Lu, Y.Y.; Gu, L., Element-free Galerkin methods, International journal for numerical methods in engineering, 37, 229-256, (1994) · Zbl 0796.73077
[4] Cheng, R.; Cheng, Y., Error estimate of the finite point method, Applied numerical mathematics, 58, 884-898, (2008) · Zbl 1145.65086
[5] Cheng, R.; Cheng, Y., Error estimates of element-free Galerkin method for potential problems, Acta physica sinica, 10, 6037-6046, (2008) · Zbl 1199.78009
[6] Cheng, Y.; Chen, M., Boundary element-free method for elasticity problems, Chinese journal of theoretical and applied mechanics, 35, 181-186, (2003)
[7] Cheng, Y.; Li, J., A meshless method with complex variables for elasticity, Acta physica sinica, 54, 4463-4471, (2005) · Zbl 1202.74163
[8] Cheng, Y.; Li, J., A complex variable meshless method for fracture problems, Science in China series G physics, mechanics & astronomy, 49, 46-59, (2006) · Zbl 1147.74410
[9] Cheng, Y.; Liew, K.M.; Kitipornchai, S., Reply to ‘comments on boundary element-free method (BEFM) and its application to two-dimensional elasticity problems, International journal for numerical methods in engineering, 78, 1258-1260, (2009) · Zbl 1183.74336
[10] Cheng, Y.; Peng, M., Boundary element-free method for elastodynamics, Science in China series G physics, mechanics & astronomy, 48, 641-657, (2005)
[11] Dai, B.; Cheng, Y., An improved local boundary integral equation method for two-dimensional potential problems, International journal of applied mechanics, 2, 421-436, (2010)
[12] Gao, H.; Cheng, Y., A complex variable meshless manifold method for fracture problems, International journal of computational methods, 7, 55-81, (2010)
[13] Kaljevic, I.; Saigal, S., An improved element free Galerkin formulation, International journal for numerical methods in engineering, 40, 2953-2974, (1997) · Zbl 0895.73079
[14] Lancaster, P.; Salkauskas, K., Surface generated by moving least squares methods, Mathematics of computation, 37, 141-158, (1981) · Zbl 0469.41005
[15] Liew, K.M.; Cheng, Y.; Kitipornchai, S., Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems, International journal of numerical methods in engineering, 65, 1310-1332, (2006) · Zbl 1147.74047
[16] Mukherjee, Y.X.; Mukherjee, S., On boundary conditions in the element-free Galerkin method, Computational mechanics, 19, 264-270, (1997) · Zbl 0884.65105
[17] Peng, M.; Liu, P.; Cheng, Y., The complex variable element-free Galerkin (CVEFG) method for two-dimensional elasticity problems, International journal of applied mechanics, 1, 367-385, (2009)
[18] Ren, H.; Cheng, Y.; Zhang, W., An improved boundary element-free method (IBEFM) for two-dimensional potential problems, Chinese physics B, 18, 4065-4073, (2009)
[19] Ren, H.; Cheng, Y.; Zhang, W., An improved boundary element-free method (IBEFM) for two-dimensional elasticity problems, Science China physics, mechanics & astronomy, 53, 758-766, (2010)
[20] Ren, H.; Cheng, Y., The interpolating element-free Galerkin (IEFG) method for two-dimensional elasticity problems, International journal of applied mechanics, 3, 735-758, (2011)
[21] Ren, H.; Cheng, Y., The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems, Engineering analysis with boundary elements, 36, 873-880, (2012) · Zbl 1352.65539
[22] Scitovski, R.; Ungar, Š.; Jukić, D., Approximating surfaces by moving total least squares method, Applied mathematics and computation, 93, 219-232, (1998) · Zbl 0943.65026
[23] Zhang, L.; Ouyang, J.; Zhang, X.; Zhang, W., On a multi-scale element-free Galerkin method for the Stokes problem, Applied mathematics and computation, 203, 745-753, (2008) · Zbl 1262.76026
[24] Zheng, B.; Dai, B., A meshless local moving Kriging method for two-dimensional solids, Applied mathematics and computation, 218, 563-573, (2011) · Zbl 1275.74033
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