本論文主要介紹一種數值方法，用以計算體外碎石術時，結石附近的壓力強度。在我們的數值方法中，水袋與人體體表的介面為使用邊界元素法的邊界，以邊界區分成兩個計算區域，分別以幾何光學與邊界積分法求解波方程去做計算。
體外碎石術中，我們用半橢球形狀的鋼碗來使由焦點位置發出的所有波束聚焦在另一個焦點位置上的結石。整個數值方法主要可以被分為三個步驟。首先，我們考慮爆震波經過鋼碗的反射到達邊界上的壓力強度值。由於，橢球有非常特殊的幾何性質，利用這個原理，我們可經由簡單的計算得到波經過反射後到達邊界上每一點的強度值。因邊界上每一點的強度值都不同，所以，我們將邊界切成三角形網格，在三角形之面積足夠小的情形下，我們取每個三角形重心位置的強度值，近似整個三角形上每一點的強度值。接著，我們再求出波穿過一個三角形孔洞的繞射壓力強度值與波由邊界到達結石所需的時間，並求出在該時間下，邊界上每個三角形給腎結石的壓力強度值。藉此，求出結石所受到的壓力值。

In this paper, we introduce a numerical method to compute the pressure intensity around the kidney stone for lithotripsy. We divide the whole computational domain into two parts by the boundary in our numerical method. We deal with one part by geometric optic, and another part be solved by boundary integral method. Using the boundary integral method to solve wave equation with the boundary condition, we transfer the 3D computational domain into 2D boundary, and only need to concentrate the wave equation on the boundary without considering the whole domain. There are three primary processes in our method.

First, we consider the pressure intensity of all points on the boundary.
Since the ellipsoid has very special geometric properties, the wave be generated by source at one of the focus, and then it must be reflected by the ellipsoid and propagate to another focus which is also the position of the kidney stone. Hence, using the way, we obtain the pressure intensity of all the points on the boundary by simple calculation.
Since there are different pressure intensity values of all the points on the boundary, we give a mesh with triangle elements on the boundary, and take the pressure intensity value at the barycenter of a triangle on the mesh as the pressure intensity of all the points on this triangle when the area of the triangle is small enough. Second, we need to compute the diffracted pressure intensity value of a triangle opening which is that a triangle opening provides for the kidney stone.
Then, we multiply the diffracted pressure intensity value of a triangle opening by its reflected pressure intensity, and obtain the final value which is that a triangle opening contributes to the kidney stone after reflection. Finally, we sum up all final intensity pressure values of
the triangle openings with their relative time, which is the time that waves propagate from the barycenter of a triangle on the boundary to the sensor point. Consequently, we get the pressure intensity value at
the kidney stone.

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