SIMPLE ELASTIC FINITE-DIFFERENCE SCHEME

This article investigates which features of the elastic finite-differe nce schemes are essential for their accuracy and which ones allow simp lifications. It is shown that the schemes employing the geometrically averaged parameters are more accurate than those using local material parameters, mainly when a discontinuity passes between the grid lines. It is also shown that the accuracy of the mixed spatial derivatives a t the internal grid points does not degrade when the number of the imp licitly employed stress values and the geometrically averaged material parameters decreases from four to two (the so-called full and short f orms, respectively), The shea and full forms give the same numerical r esults, while 50% of the arithmetic operations are saved with the shor t one. However, at the free-surface points, such a simplification is n ot permitted, and the full form should be used. Based on these results , a new simple elastic scheme (called PS2) is suggested.