CAJ | 학술논문

本文利用第二代小波多尺度分解和快速变换的特点,构造自适应计算网格.对初始计算网格上的数值解进行第二代小波变换,得到数值解对应的小波系数宅问.小波系数的大小表示相邻网格上数值变化率,小波系数大的区域网格点上的数值解变化梯度大.当小波系数大于等于预设的阈值时,在小波系数对应的网格点周围插入新的计算网格点,通过阈值可以实现网格的细化,得到多尺度下层层嵌套的细化自适应网格;由有限差分法得到相应网格点的空间导数.比较数值算例得到的波场快照和计算时间,验证了该方法的有效性.
본문이용제이대소파다척도분해화쾌속변환적특점,구조자괄응계산망격.대초시계산망격상적수치해진행제이대소파변환,득도수치해대응적소파계수택문.소파계수적대소표시상린망격상수치변화솔,소파계수대적구역망격점상적수치해변화제도대.당소파계수대우등우예설적역치시,재소파계수대응적망격점주위삽입신적계산망격점,통과역치가이실현망격적세화,득도다척도하층층감투적세화자괄응망격;유유한차분법득도상응망격점적공간도수.비교수치산례득도적파장쾌조화계산시간,험증료해방법적유효성.
In this paper,it takes second generation wavelet as a tool that structure adaptive mesh,because second generation wavelet has multilevel decomposition and the fast transformation of the characteristics. First,we make value of wave fields on coarse mesh processed second generation wavelet transform,which obtained wavelet coefficients corresponding to the space in which each wavelet coefficients with the real physical space on the discrete grid.These coefficients should decay quickly to zero in the smooth regions,and should be large only in the region where the gradient of u(x) is large.In order to better numerical simulation of the mutation of the region,we have set up a wavelet threshold to determine the grid for each point corresponding to the size of the wavelet coefficients,when the wavelet coefficients greater than or equal to the threshold,the wavelet coefficients corresponding to the grid together with the surrounding The new grid computing,the threshold to control to be multilevel under layers of nested adaptive mesh refinement,and to use adaptive mesh refinement algorithm to calculate the space derivative.By simulating the wave propagation in media,these results have proven the effectiveness of the method.