ANN-based Mesh-free Method to Solve Partial Differential Equations

2021 ◽  
Author(s):  
Filipi Teixeira Kunz ◽  
Ney Rafael Secco
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Mesh Free ◽  
Mesh Free Method

Continuous Solution of Partial Differential Equations on Non-Rectangular and Non-Continuous Geometry

2014 ◽  
Author(s):  
P. Venkataraman
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Continuous Solution ◽  
Finite Difference Methods ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Mesh Free ◽  
Numeric Calculation ◽  
Linear And Nonlinear

A high order continuous solution is obtained for partial differential equations on non-rectangular and non-continuous domain using Bézier functions. This is a mesh free alternative to finite element or finite difference methods that are normally used to solve such problems. The problem is handled without any transformation and the setup is direct, simple, and involves minimizing the error in the residuals of the differential equations along with the error in the boundary conditions over the domain. The solution can be expressed in polynomial form. The effort is same for linear and nonlinear partial differential equations. The procedure is developed as a combination of symbolic and numeric calculation. The solution is obtained through the application of standard unconstrained optimization. A constrained approach is also developed for nonlinear partial differential equations. Examples include linear and nonlinear partial differential equations. The solution for linear partial differential equations is compared to finite element solutions from COMSOL.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
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