TY - JOUR AU - Rao, Ling AU - Chang, Shih-Sen PY - 2018 TI - Numerical solution for a nonlinear obstacle problem JO - Journal of Nonlinear Sciences and Applications SP - 1302--1312 VL - 11 IS - 12 AB - A monotone iterations algorithm combined with the finite difference method is constructed for an obstacle problem with semilinear elliptic partial differential equations of second order. By means of Dirac delta function to improve the computation procedure of the discretization, the finite difference method is still practicable even though the obstacle boundary is irregular. The numerical simulations show that our proposed methods are feasible and effective for the nonlinear obstacle problem. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.12.02 DO - 10.22436/jnsa.011.12.02 ID - Rao2018 ER - TY - JOUR TI - A finite element approach for the immersed boundary method AU - D. Boffi AU - L. Gastaldi JO - Comput. Structures PY - 2003 DA - 2003// VL - 81 ID - Boffi2003 ER - TY - JOUR TI - Generalized finite difference method for solving two-dimensional non-linear obstacle problems AU - H.-F. Chan AU - C.-M. Fan AU - C.-W. Kuo JO - Eng. Anal. Bound. Elem. PY - 2013 DA - 2013// VL - 37 ID - Chan2013 ER - TY - JOUR TI - Incompressible flows in elastic domains: an immersed boundary method approach AU - S. A. Enriquez-Remigio AU - A. M. Roma JO - Appl. Math. Model. PY - 2005 DA - 2005// VL - 29 ID - Enriquez-Remigio2005 ER - TY - BOOK TI - Numerical analysis of variational inequalities AU - R. Glowinski AU - J.-L. Lions AU - R. Tremolieres PB - North-Holland Publishing Co. PY - 1976 DA - 1976// CY - Amsterdam-New York ID - Glowinski1976 ER - TY - JOUR TI - A fictitious domain method for Dirichlet problem and applications AU - R. Glowinski AU - T.-W. Pan AU - J. Periaux JO - Comput. Methods Appl. Mech. Engrg. PY - 1994 DA - 1994// VL - 111 ID - Glowinski1994 ER - TY - JOUR TI - Monotone iterations for nonlinear obstacle problem AU - P. Korman AU - A. W. Leung AU - S. Stojanovic JO - J. Austral. Math. Soc. Ser. B PY - 1990 DA - 1990// VL - 31 ID - Korman1990 ER - TY - JOUR TI - Numerical analysis of blood flow in the heart AU - C. S. Peskin JO - J. Computational Phys. PY - 1977 DA - 1977// VL - 25 ID - Peskin1977 ER - TY - JOUR TI - The immersed boundary method AU - C. S. Peskin JO - Acta Numer. PY - 2002 DA - 2002// VL - 11 ID - Peskin2002 ER - TY - JOUR TI - The technique of the immersed boundary method: application to solving shape optimization problem AU - L. Rao AU - H. Q. Chen JO - J. Appl. Math. Phy. PY - 2017 DA - 2017// VL - 5 ID - Rao2017 ER - TY - JOUR TI - On the solution of some boundary value problems on high performance computers by fictitious domain method AU - V. K. Saulev JO - Siberian Math. J. PY - 1963 DA - 1963// VL - 4 ID - Saulev1963 ER - TY - JOUR TI - Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method AU - A. L. F. L. E. Silva AU - A. Silveira-Neto AU - J. J. R. Damasceno JO - J. Computational Phys. PY - 2003 DA - 2003// VL - 189 ID - Silva2003 ER -