An Analysis of the Axisymmetric Modified Helmholtz Equation by Using the Boundary Element Method

1988 ◽  
pp. 105-113
Author(s):  
Masanori Tsuchimoto ◽  
Toshihisa Honma ◽  
Atsuhiko Yoneta ◽  
Satoru Tanaka ◽  
Kenzo Miya
Keyword(s):  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Modified Helmholtz Equation ◽  
Element Method

scholarly journals Dual Reciprocity Boundary Element Method untuk Menyelesaikan Masalah Infiltrasi Stasioner pada Saluran Datar Periodik

2021 ◽  
Vol 4 (1) ◽  
pp. 30
Author(s):  
M. Megasari
Keyword(s):  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Analytic Solution ◽  
Flat Channel ◽  
Modified Helmholtz Equation ◽  
Collocation Points ◽  
Kirchhoff Transformation ◽  
Richard's Equation ◽  
Element Method

Abstrak. Penelitian ini membahas tentang penyelesaian masalah infiltrasi stasioner dari saluran datar dengan Dual Reciprocity Boundary Element Method (DRBEM). Persamaan pembangun untuk masalah ini adalah persamaan Richard. Menggunakan transformasi Kirchhoff dan relasi eksponensial konduktifitas hidrolik, persamaan Richard ditransformasi ke dalam persamaan infiltrasi stasioner dalam Matric Flux Potential (MFP). Persamaan infiltrasi dalam MFP selanjutnya diubah ke dalam persamaan Helmholtz termodifikasi. Model matematika infiltrasi stasioner pada saluran datar berbentuk Masalah Syarat batas Helmholtz termodifikasi Solusi numerik diperoleh dengan menyelesaikan persamaan Helmholtz termodifikasi menggunakan Dual Reciprocity Boundary Element Method (DRBEM) dengan pengambilan jumlah titik kolokasi eksterior dan interior yang bervariasi. Lebih lanjut, solusi numerik dan solusi analitik dibandingkan..Kata Kunci: Infiltrasi, saluran datar, persamaan helmholtz termodifikasi, DRBEM.Abstract. This research discusses about the problem solving of steady infiltration problem from flat channel with Dual Reciprocity Boundary Element Method (DRBEM). The governing equation for this problem is Richard’s equation. Using Kirchhoff transformation and exponential hydraulic conductivity relation, Richard’s equation is transformed into steady infiltration equation in the form of MFP. Infiltration equation in the form of MFP is then transformed to modified Helmholtz equation. A mathematical model of steady infiltration from flat channel in the form of boundary condition problem of modified Helmholtz EQUATION. Numerical solution is obtained by solving modified Helmholtz equation by using Dual Reciprocity Boundary Element Method (DRBEM) with various number of exterior and interior collocation points. Moreover, numerical and analytic solution are then compared.Keywords: infiltration, flat channel, modified Helmholtz equation, DRBEM

scholarly journals PENENTUAN JENIS FUNGSI BASIS RADIAL DALAM DUAL RECIPROCITY BOUNDARY ELEMENT METHOD

2021 ◽  
Vol 21 (1) ◽  
pp. 53
Author(s):  
Millatuz Zahroh
Keyword(s):  
Exact Solution ◽  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Boundary Integral ◽  
Reciprocal Relation ◽  
Modified Helmholtz Equation ◽  
Domain Integral ◽  
Linear Types ◽  
Element Method

Problems involving modified Helmholtz equation are considered in this paper. To solve the problem numerically, dual reciprocity boundary element method (DRBEM) is employed. Some stage have been passed, using reciprocal relation to approximate boundary integral and domain integral in modified Helmholtz equation . Until, linear equation system are obtained in matrix form. MATLAB is used to calculate the solutions of Solutions of are compared between the exact solution and the numerical solution of modified Helmholtz equation. The numerical results are based on the using of three types of radial basis function to approximate domain integral, such as polinomial, poliharmonik spline and linear types. The solutions show that the polinomial and poliharmonik spline types are more stable and approach to exact solution than linear types.

scholarly journals DUAL RECIPROCITY BOUNDARY ELEMENT METHOD (DRBEM) DENGAN PREDIKTOR-KOREKTOR UNTUK MASALAH INFILTRASI STASIONER PADA SALURAN DENGAN LAPISAN IMPERMEABEL DENGAN ROOT WATER UPTAKE

2019 ◽  
Vol 4 (1) ◽  
pp. 19
Author(s):  
Irma Novalinda Nasution
Keyword(s):  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Numerical Solution ◽  
Boundary Element ◽  
Water Uptake ◽  
Root Water Uptake ◽  
Dimensionless Parameters ◽  
Modified Helmholtz Equation ◽  
Predictor Corrector ◽  
Element Method

This study  aims to discussed  about Dual Reciprocity Boundary Element Method (DRBEM) with a predictor-corrector for steady infiltration problems with impermeabel layer with root water uptake in homogeneous soils. Steady infiltration in homogeneous soils is governed by Richard equation. This equation is transformed using a set of transformation including Khirchoff, dimensionless variabels and dimensionless parameters into a type of modified Helmholtz equation. Furthermore with DRBEM, numerical solution of modified Helmholtz equation obtained. The proposed method is tested on problem involved infiltration from rectangular and trapezoidal channels with impermeabel layer with root water uptake. Keyword : infiltration, root water uptake, modified Helmholtz equation, Richard equation, DRBEM

Sign in / Sign up

Export Citation Format

Share Document