GRKPM: Theory and Applications in Laminated Composite Plates and Nonlinear Evolutionary Partial Differential Equations With Large Gradients, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract
Reproducing kernel particle method (RKPM) is a meshfree method for solving various differential equations. RKPM is based on pure mathematics; therefore, it is in the center of attention of many scientists. One major problem in RKPM is satisfying the essential boundary conditions (EBCs) involving the derivative of the field function. This problem is considered herein and its solution is proposed. To this end, two actions should be undertaken. First, the concept of Hermitian interpolation is employed to add the derivative term to the reproducing equation of RKPM and a new meshless method called gradient RKPM (GRKPM) is introduced. Second, the corrected collocation method is modified so...
Cataloging briefGRKPM: Theory and Applications in Laminated Composite Plates and Nonlinear Evolutionary Partial Differential Equations With Large Gradients, Ph.D. Dissertation Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract
Reproducing kernel particle method (RKPM) is a meshfree method for solving various differential equations. RKPM is based on pure mathematics; therefore, it is in the center of attention of many scientists. One major problem in RKPM is satisfying the essential boundary conditions (EBCs) involving the derivative of the field function. This problem is considered herein and its solution is proposed. To this end, two actions should be undertaken. First, the concept of Hermitian interpolation is employed to add the derivative term to the reproducing equation of RKPM and a new meshless method called gradient RKPM (GRKPM) is introduced. Second, the corrected collocation method is modified so...
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