scholarly journals Multi-Asset Barrier Options Pricing by Collocation BEM (with Matlab® Code)

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 301
Author(s):  
Alessandra Aimi ◽  
Chiara Guardasoni
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Analytical Method ◽  
Numerical Results ◽  
Options Pricing ◽  
Barrier Options ◽  
Element Method

In this paper, we extend the SABO technique (Semi-Analytical method for Barrier Options), based on collocation Boundary Element Method (BEM), to the pricing of Barrier Options with payoff dependent on more than one asset. The efficiency and accuracy already revealed in the case of a single asset is confirmed by the presented numerical results.

A 3D BOUNDARY ELEMENT METHOD FOR DETERMINATION OF ACOUSTIC EIGENFREQUENCIES CONSIDERING ADMITTANCE BOUNDARY CONDITIONS

1993 ◽  
Vol 01 (04) ◽  
pp. 455-468 ◽  
Author(s):  
Z. S. CHEN ◽  
G. HOFSTETTER ◽  
H. A. MANG
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Large Scale ◽  
Numerical Study ◽  
Numerical Algorithms ◽  
Numerical Results ◽  
Simple Problem ◽  
Element Method

A 3D boundary element method for the determination of the acoustic eigenfrequencies of car compartments, characterized by a unified treatment of Robin, Dirichlet, and Neumann boundary conditions, is presented. The drawback of frequency-dependent matrices of the eigenvalue problem is overcome by means of the Particular Integral Method. Thus, the standard numerical algorithms for the extraction of eigenvalues can be applied. The numerical study contains both a comparison of numerical results with analytical solutions of a simple problem with different types of boundary conditions and a comparison of numerical results of a large-scale problem with respective numerical results, computed on the basis of the finite element method. In addition, for the latter example, different numerical algorithms for the eigenvalue extraction are examined.

Numerical Integral Independent of Frequency in the Boundary Element Method for Acoustic Scattering

2013 ◽  
Vol 444-445 ◽  
pp. 650-654
Author(s):  
Zai You Yan ◽  
Chuan Zhen Li
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Acoustic Scattering ◽  
Normal Derivative ◽  
Numerical Results ◽  
New Technique ◽  
Computational Time ◽  
Unknown Variable ◽  
Numerical Integral ◽  
Element Method

Fast algorithm for multi-frequency numerical integration in the simulation of acoustic scattering from rigid object by the boundary element method is presented. Normal derivative of the free-space Greens function is partially approximated with the unknown variable by a set of shape functions. As a result, the numerical integral is independent of frequency and need be calculated only at the first frequency step. Singular integral can be computed using the same procedure as that applied in the conventional boundary element method. Computational efficiency and accuracy of the new technique are demonstrated by an example. Numerical results obtained using the new technique are compared with the corresponding analytical solutions and numerical results obtained using the conventional boundary element method. The new technique works well and saves a lot of computational time in the process of generation of coefficient matrices for multi-frequency analysis.

Fast Calculation of Far-Field Sound Directivity Based on Fast Multipole Boundary Element Method

2020 ◽  
Vol 28 (04) ◽  
pp. 1950024
Author(s):  
Takayuki Masumoto ◽  
Yosuke Yasuda ◽  
Naohisa Inoue ◽  
Tetsuya Sakuma
Keyword(s):  
Boundary Element Method ◽  
High Resolution ◽  
Boundary Element ◽  
Conventional Method ◽  
Numerical Results ◽  
Computational Time ◽  
Fast Method ◽  
Far Field ◽  
Fast Multipole ◽  
Element Method

A fast method for calculating sound radiation/reflection directivities at high resolution in the infinite far field is proposed with the use of the fast multipole boundary element method (FMBEM). This method calculates directivities using direction-dependent coefficients called outgoing coefficients, which are obtained in the calculation process of the matrix-vector products in the FMBEM. Since the outgoing coefficients are generally calculated for a large number of directions high-resolution directivities can be easily obtained with extremely small computational cost and minor modifications in the FMBEM program codes. It is confirmed via comparison with the numerical results using the conventional method that the proposed method can calculate directivities at infinity. Numerical results also show that the computational time for the proposed method is significantly shorter than that for the conventional method with no addition of the required memory.

Evolution of Pressure on Bearing's Surface in Dislocated Single Floating Ring Bearing

2012 ◽  
Vol 580 ◽  
pp. 428-431
Author(s):  
Xue Hui Wang ◽  
Yu Jie Dai
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Results ◽  
Element Method

The pressure on bearing’s surface in the dislocated single floating ring bearing with different radius of floating ring (Rf) and velocity of floating ring (Uf) were simulated by boundary element method (BEM). The numerical results indicate that the pressure on bearing increases with the increases of Ufwhen displacement of bearing (DR) is fixed. The pressure on bearing increases with the increases of Rfwhen DR is fixed. The pressure on bearing increases with the increases of DR when Rfis fixed.

Numerical Simulation of Frictional Dissipation in the Dislocated Single Floating Ring Bearing

2012 ◽  
Vol 580 ◽  
pp. 59-62
Author(s):  
Xue Hui Wang ◽  
Yu Jie Dai ◽  
Jiu Qing Hao
Keyword(s):  
Numerical Simulation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Results ◽  
Numerical Efficiency ◽  
Frictional Dissipation ◽  
Simulation Error ◽  
Element Method

The frictional dissipation in the dislocated single floating ring bearing is simulated by boundary element method (BEM). The advantage of BEM is that it can reduce the numerical simulation error and increase the numerical efficiency. The numerical results indicate that the total frictional dissipation decreases with the increases of the floating ring’s velocity and never change when the radius of the floating ring Rf=0.4. The evolution of total frictional dissipation is similar with the bearing’s frictional dissipation.

A Boundary Element Analysis of Metal Extrusion Processes

1987 ◽  
Vol 54 (2) ◽  
pp. 335-340 ◽  
Author(s):  
A. Chandra ◽  
S. Mukherjee
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Results ◽  
Element Analysis ◽  
Geometrical Nonlinearities ◽  
The Subject ◽  
Boundary Element Analysis ◽  
Metal Extrusion ◽  
Element Method

The subject of this paper is an analysis of metal extrusion processes by the boundary element method (BEM). It is demonstrated here that the BEM can be used to analyze, efficiently and accurately, this complicated class of problems including both material and geometrical nonlinearities. Numerical results for sample problems of plane extrusion of aluminum bars, obtained by the BEM, are presented and discussed in this paper. The BEM results are compared against FEM results for the same sample problems. The FEM results were reported by the authors in a previous publication.

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