INVALIDITY OF DECOUPLING A BIHARMONIC EQUATION TO TWO POISSON EQUATIONS ON NON-CONVEX POLYGONS
INVALIDITY OF DECOUPLING A BIHARMONIC EQUATION TO TWO POISSON EQUATIONS ON NON-CONVEX POLYGONS
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发表时间：
2007
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通讯作者：
Sheng Zhang;Zhimin Zhang
中科院分区：
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作者：
Sheng Zhang;Zhimin Zhang
阐明了将一个双调和方程的边值问题转化为多边形区域上两个Poisson方程的方法的有效性。该方法提供了一种用泊松方程求解器计算简支多边形板挠度的方法。我们表明，这种解耦是无效的，如果多边形域不是凸的。它可能失败，即使右手边的功能是无限光滑，并支持远离凹角。
We clarify the validity of a method that decouples a boundary value problem of biharmonic equation to two Poisson equations on polygonal domains. The method provides a way of computing deflections of simply supported polygonal plates by using Poisson solvers. We show that such decoupling is not valid if the polygonal domain is not convex. It may fail even when the right hand side function is infinitely smooth and supported away from the reentrant corners.