本文選題：數(shù)值流形法　切入點(diǎn)：加密物理片　出處：《巖土力學(xué)》2017年04期 　論文類型：期刊論文

【摘要】：數(shù)值流形法的數(shù)學(xué)網(wǎng)格不需要適應(yīng)求解域內(nèi)各種不連續(xù)界面和邊界,因此,總可以用規(guī)則的結(jié)構(gòu)化網(wǎng)格建立數(shù)學(xué)覆蓋。但對(duì)于大多數(shù)問(wèn)題,在整個(gè)求解域上布置統(tǒng)一密度的網(wǎng)格顯得浪費(fèi)。因此,需要研究在結(jié)構(gòu)化網(wǎng)格上實(shí)施局部加密,建立了加密物理片的方法用以解決這一問(wèn)題。具體的實(shí)施過(guò)程中,確定了需要加密的區(qū)域后,先在這些區(qū)域布置規(guī)則的精細(xì)網(wǎng)格,然后找到這些區(qū)域中包含的原始網(wǎng)格中的物理片,用精細(xì)網(wǎng)格上建立的插值代替被加密物理片上的局部近似,從而提高了局部近似的階次。數(shù)值算例結(jié)果表明,該方法收斂性良好。另外,如果所有物理片上的局部近似都采用0階多項(xiàng)式(常數(shù)),那么將會(huì)得到正定的剛度矩陣。
[Abstract]:The mathematical mesh of the numerical manifold method does not need to be adapted to solve various discontinuous interfaces and boundaries in the domain, so it is always possible to establish a mathematical cover with regular structured meshes. But for most problems, It is wasteful to arrange uniform density grids in the whole solution domain. Therefore, it is necessary to study the implementation of local encryption on structured grids, and to establish a method of encrypting physical slices to solve this problem. After the regions that need encryption are determined, regular fine grids are arranged in these areas first, then the physical slices in the original grids contained in these areas are found, and the interpolation established on the fine grids is used to replace the local approximation on the encrypted physical slices. As a result, the order of local approximation is improved. The numerical results show that the method converges well. In addition, if all the local approximations on the physical chip adopt the polynomial of order 0 (constant), then the positive definite stiffness matrix will be obtained.
【作者單位】： 中國(guó)科學(xué)院武漢巖土力學(xué)研究所巖土力學(xué)與工程國(guó)家重點(diǎn)實(shí)驗(yàn)室;湖北省水利水電科學(xué)研究院;
【基金】：國(guó)家自然科學(xué)基金項(xiàng)目(No.11572009,No.51538001)~~
【分類號(hào)】：O241.3
，

本文編號(hào)：1591762