scholarly journals Local weak form meshless techniques based on the radial point interpolation (RPI) method and local boundary integral equation (LBIE) method to evaluate European and American options

2015 ◽  
Vol 22 (1-3) ◽  
pp. 1178-1200 ◽  
Author(s):  
Jamal Amani Rad ◽  
Kourosh Parand ◽  
Saeid Abbasbandy
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
American Options ◽  
Weak Form ◽  
Boundary Integral ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Local Weak Form

A New Test Function for Acoustic Computations with Meshless Methods

2019 ◽  
Vol 27 (01) ◽  
pp. 1940001
Author(s):  
Hakan Dogan ◽  
Martin Ochmann
Keyword(s):  
Integral Equation ◽  
Weak Form ◽  
Meshless Methods ◽  
Boundary Integral ◽  
Computational Time ◽  
Test Functions ◽  
Test Function ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Local Weak Form

The meshless local Petrov–Galerkin (MLPG) and the local boundary integral equation (LBIE) methods has been introduced approximately three decades ago. These methods are based on writing the local weak form of the governing equation and performing subsequent numerical integration and interpolations in the local subdomains. A key step is the choice of the test function in the local weak form, which has historically led to several different formulations regarding the final form of the local integrals. Considering the application of the methods to acoustics, four different test functions have been employed so far in the literature; all of these approaches resulted in formulations which contain domain integrals. In this paper, we present a new test function to be used in meshless methods, which yields a simple form of the local integral equation without domain integrals and provides significant improvement in terms of the computational time and CPU requirements. The efficiency and the accuracy of the new method are presented and compared with the previous methods.

AN IMPROVED LOCAL BOUNDARY INTEGRAL EQUATION METHOD FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

2010 ◽  
Vol 02 (02) ◽  
pp. 421-436 ◽  
Author(s):  
BAODONG DAI ◽  
YUMIN CHENG
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Computational Efficiency ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Potential Problems

Combining the local boundary integral equation with the improved moving least-squares (IMLS) approximation, an improved local boundary integral equation (ILBIE) method for two-dimensional potential problems is presented in this paper. In the IMLS approximation, the weighted orthogonal functions are used as basis functions. The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares (MLS) approximation and does not lead to an ill-conditioned equations system. The corresponding formulae of the ILBIE method are obtained. Comparing with the conventional local boundary integral equation (LBIE) method, the ILBIE method is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be implemented directly and easily as in the finite element method. The ILBIE method has greater computational efficiency and precision. Some numerical examples to demonstrate the efficiency of the method are presented in this paper.

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