【摘要】：區(qū)域分解算法將大規(guī)模問題轉(zhuǎn)化成若干小問題進(jìn)行求解,極大縮小計(jì)算規(guī)模和節(jié)省內(nèi)存空間,已成為解決大規(guī)模復(fù)雜數(shù)值問題的有力手段.本文以大地電磁法(MT)二維正演為例,將二維求解區(qū)域劃分為若干重疊子域,子域采用有限差分法進(jìn)行離散并采用LU直接分解法進(jìn)行獨(dú)立求解,然后運(yùn)用Schwarz交替法實(shí)現(xiàn)重疊區(qū)域解的傳遞和更新,從而實(shí)現(xiàn)大地電磁法二維正演數(shù)值模擬.對(duì)典型低阻地電模型進(jìn)行數(shù)值模擬實(shí)驗(yàn)并與傳統(tǒng)全域正演算法相比,表明本文算法的準(zhǔn)確性和可行性;同時(shí)能夠極大節(jié)省計(jì)算機(jī)內(nèi)存及減小CPU計(jì)算時(shí)間.另外對(duì)重疊區(qū)域算法的影響規(guī)律研究表明,本文算法所需內(nèi)存隨剖分重疊子域數(shù)目增多而降低,CPU計(jì)算時(shí)間隨剖分重疊子域數(shù)目增多而先減小后增加;重疊子域組合方式和重疊規(guī)模大小對(duì)計(jì)算效率有一定影響,需進(jìn)行合理優(yōu)化.因此本文提出的算法為電磁法三維大規(guī)模問題的正反演計(jì)算提供了一種新的思路.
[Abstract]:Domain decomposition algorithm has become a powerful method to solve large scale complex numerical problems by transforming large scale problems into some small problems and greatly reducing the scale of computation and saving memory space. In this paper, the (MT) two-dimensional forward modeling of magnetotelluric method is taken as an example, the two-dimensional solution region is divided into several overlapping subdomains, the subdomains are discretized by the finite difference method and the LU direct decomposition method is used to solve them independently. Then the Schwarz alternating method is used to transfer and update the solution of overlapped region, thus the two-dimensional forward numerical simulation of magnetotelluric method is realized. Numerical simulation experiments on typical low-resistivity geoelectric models show that the proposed algorithm is accurate and feasible compared with the traditional global forward algorithm, and can greatly save computer memory and reduce CPU computing time. In addition, the study on the effect of overlapping region algorithm shows that the memory required by this algorithm decreases with the number of overlapping subfields, and the CPU computing time decreases first and then increases with the number of overlapping subfields. The combination of overlapping subdomains and the size of overlapped subdomains have a certain effect on the calculation efficiency, which need to be optimized reasonably. Therefore, the algorithm presented in this paper provides a new idea for the forward inversion of electromagnetic method for three dimensional large scale problems.
【作者單位】： 東華理工大學(xué)放射性地質(zhì)與勘探技術(shù)國防重點(diǎn)學(xué)科實(shí)驗(yàn)室;
【基金】：國家青年基金項(xiàng)目(41404057) 國家自然科學(xué)基金項(xiàng)目(41164003,41674077)聯(lián)合資助
【分類號(hào)】：P631.325

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