Consider 2D Laplace’s equation in a bounded simply-connected domain S, and solve it by the method of fundamental solutions (MFS). The source nodes must be located outside the domain boundary Γ (= S). How to select better source nodes is essential to the MFS in both theory and computation. In the standard MFS, source nodes are located on a closed contour outside Γ, called pseudo-boundaries. Circular/elliptic pseudo-boundaries are widely used, but non-circular/non-elliptic pseudo-boundaries offer better numerical performance for complicated shapes of Γ and singular solutions. For the latter, however, how to find their better shapes is challenging. In this paper, we study new locations of source nodes along pseudo radial-lines outside Γ. Denote the source nodes by (Ri , φ i ) in polar coordinates, where Ri > ρmax = max ρ|Γ

中文翻译：

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求解拉普拉斯方程的基本解法的源节点的新位置；伪径向线

考虑有界单连通域 S 中的二维拉普拉斯方程，并通过基本解法 (MFS) 求解。源节点必须位于域边界 Γ (= S) 之外。如何选择更好的源节点对于 MFS 的理论和计算都是至关重要的。在标准 MFS 中，源节点位于 Γ 之外的闭合轮廓上，称为伪边界。圆形/椭圆伪边界被广泛使用，但非圆形/非椭圆伪边界为复杂形状的 Γ 和奇异解提供更好的数值性能。然而，对于后者，如何找到更好的形状是具有挑战性的。在本文中，我们研究了 Γ 外沿伪径向线的源节点的新位置。在极坐标中用 (Ri , φ i ) 表示源节点，其中 Ri > ρmax = max ρ|Γ