多孔结构热传导问题的并行多尺度分析  

Parallel multiscale analysis of heat conduction equation in perforated domain

作　　者：曹信信 王辛[1] CAO Xinxin;WANG Xin(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2018年第3期519-540,共22页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11301329)

摘　　要：多孔材料在航空航天、汽车、机械领域应用广泛,由于其微结构的多孔性,需要发展多尺度算法用于其性能预测.本文先应用Fourier变换将多孔区域的热传导问题转换为频域空间的复值问题,然后对频域问题做多尺度渐近分析,通过构造边界层证明了频域方程的多尺度截断误差估计.进一步,本文利用孔洞填充思想提出了一套在无孔区域上研究多孔区域的统一的多尺度方法,构造了一套预测多孔材料热性能的新的并行多尺度算法,结合逆积分变换给出了整个算法的误差估计.Perforated material is now widely used in aerospace engineering,au-tomotive industry and machinery field.It is important to develop the multiscale algorithm to predict its performance.In this paper,the Fourier transform is first applied to the heat conduction equation in perforated domain to obtain complex-valued problems in frequency domain.Then,the multiscale asymptotic analysis is presented for the frequency problems and the multiscale trucation error esti-mate is derived by the method of boundary layer technique.Furthermore,with the hole-filling method,a uniform multiscale method in non-perforated domain is proposed to study the problem in perforated domain.A novel parallel multiscale algorithm to predict the performance of perforated material is then constructed.The full error estimate of the presented algorithm is proved with the inverse integral transformation.

关 键 词：多孔材料 多孔区域 多尺度渐近分析 孔洞填充 

分 类 号：O241.82[理学—计算数学]