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On the solution of evolution equations based on multigrid and explicit iterative methods

机译：基于多重网格和显式迭代方法的演化方程解

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摘要

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.
机译：研究了两种解决三维抛物线方程初边值问题的方案。一个是隐式的，可以使用multigrid方法求解，另一个是显式的迭代，并且基于Chebyshev多项式的最优性质。在显式迭代方案中，迭代步数和迭代参数的选择是基于近似条件和稳定性条件，而不是基于对隐式方案求解的迭代收敛优化。多重网格方案的特征包括在方程中系数不连续的情况下实施网格间转移算子，并使平滑过程适应差分算子的频谱。比较了这些方案所产生的结果，这些结果适用于各向异性不连续系数的模型问题。

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