A Numerical Approach for Determination of Sources in Reactive Transport Equations
A new numerical approach for locating the source and quantifying its power is presented and studied. The proposed method may also be helpful when dealing with other transport problems.
The method uses a numerical integration technique to evaluate a linear functional arising from the solution of the adjoint problem. It is shown that using the solution of the adjoint equation an efficient numerical method can be constructed (a method, which is less time comsumpting than the usual schemes applied for solving the original problem). Our approach leads to a well-conditioned numerical problem.
A number of numerical tests are performed for a one-dimentional problem with a linear advection part. The results are compared with results obtained when solving the original problem. The code which realizes the presented method is written in FORTRAN 77.
KeywordsNumerical Scheme Original Problem Elliptic Operator Adjoint Equation Adjoint Problem
Unable to display preview. Download preview PDF.
- N.S. Bahvalov, On the optimal estimations of convergence of the quadrature processes and integration methods, Numerical methods for solving differential and integral equations Nauka, Moscow, 1964, pp. 5–63.Google Scholar
- Bitzadze A.V., Equations of the Mathematical Physics, Nauka, 1982.Google Scholar
- I. Dimov, O. Tonev, Monte Carlo methods with overconvergent probable error, in Numerical Methods and Applications, Proc. of Intern.Conf on Numerical Methods and Appl.,Sofia, (Publ. House of Bulg. Acad. Sci, Sofia, 1989), pp. 116–120.Google Scholar
- S.M. Ermakov, G.A. Mikhailov Statistical Modeling, Nauka, Moscow, 1982.Google Scholar
- G. A. Mikhailov A new Monte Carlo algorithm for estimating the maximum eigenvalue of an integral operator, Docl. Acad. Nauk SSSR, 191, No 5 (1970), pp. 993–996.Google Scholar
- G.A. Mikhailov, Optimization of the “weight” Monte Carlo methods Nauka, Moscow, 1987.Google Scholar
- Tikhonov A.N., Samarski A.A., Equations of the Mathematical Physics. Moskow, Nauka, 1977.Google Scholar