Autor: J.-E. Nordtvedt, Sam Subbey
Rok vydání: 2002
Předmět:
Zdroj: Computational Geosciences. 6:207-224
ISSN: 1420-0597
DOI: 10.1023/a:1019943419164
Popis: The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form ∫ a x K(x,t)f(t) dt=g(x),x∈[a,b],(1) where the kernel K is known exactly and given by the underlying mathematical model. g is only known with a limited degree of accuracy in a finite and discrete set of points x 1,...,x M . However, the sought function f(t) is continuous. By the nature of the right-hand side, g(x), equation (1) is a discrete inverse problem which is ill-posed in the sense of Hadamard [9]. By a parameterization of the sought function, equation (1) reduces to a system of linear equations of the form Ac=b+ e, where b is the observation vector and A arises from discretization of the forward problem. e is the error vector associated with b, and c contains the model parameters. The matrix A is usually ill-conditioned. The ill-conditioning is closely connected to the parameterization of the problem [23]. In this paper a semi-iterative regularization method for solving the Volterra integral equation in the l2-norm, namely, Brakhage's ν-method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.
Databáze: OpenAIRE
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