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Mechanical quadrature methods and their extrapolations for solving boundary integral equations of the conductivity problem with discontinuous media

机译：求解介质不连续性电导率问题的边界积分方程的机械正交方法及其外推法

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摘要

Mixed boundary value problems of the conductivity equation ▽.(γ▽u) = 0 with discontinuous media are converted into boundary integral equations by using the single layer potential. For solving the induced boundary integral equations, a mechanical quadrature method is proposed for periodic Fredholm integral equations with logarithmic singularity, which possesses a high order accuracy O(h~3), less computational complexity and asymptotic expansion of the errors. By means of Richardson extrapolation, an approximation with a higher accuracy order O(h~5) is obtained. Moreover, a posteriori error estimate for the algorithm is derived, which can be used to constructed adaptive algorithm. Several numerical examples show that the accuracy order of approximation is very high, the extrapolation and a posteriori error estimates are also very effective.
机译：使用单层电势将具有不连续介质的电导率方程▽。（γ▽u）= 0的混合边值问题转换为边界积分方程。为求解诱导边界积分方程，提出了一种具有对数奇异性的周期Fredholm积分方程的机械正交方法，该方法具有高阶精度O（h〜3），计算复杂度小，误差渐近扩展。通过理查森外推，获得具有较高精度阶数O（h〜5）的近似值。此外，推导了该算法的后验误差估计，可用于构造自适应算法。几个数值例子表明，逼近的精确度阶数很高，外推和后验误差估计也非常有效。

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