Eigenvalues for the semi-circulant preconditioning of elliptic operators with the variable coefficients
نویسندگان
چکیده
We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by Lvu := −∆u + a(x, y)ux + b(x, y)uy + d(x, y)u, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator Lcu is constructed by using the leading term of Lvu plus the constant reaction term such that Lcu := −∆u + dcu. Using the field of values arguments, we show that the maximum and minimum eigenvalues of the preconditioned matrix behave similarly as the case of the second-order elliptic operator with constant coefficients. Some numerical evidences are also provided.
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