TY - JOUR
T1 - THE HETEROGENEOUS MULTISCALE METHODS
AU - Weinan, E.
AU - Engquist, Bjorn
N1 - Publisher Copyright:
© 2003 International Press
PY - 2003
Y1 - 2003
N2 - The heterogeneous multiscale method (HMM) is presented as a general methodology for the efficient numerical computation of problems with multiscales and multiphysics on multigrids. Both variational and dynamic problems are considered. The method relies on an efficient coupling between the macroscopic and microscopic models. In cases when the macroscopic model is not explicitly available or invalid, the microscopic solver is used to supply the necessary data for the macroscopic model. Scale separation can be exploited to considerably reduce the complexity of the microscopic solver. Besides unifying several existing multiscale methods such as the ab initio molecular dynamics [13], quasicontinuum methods [73, 69, 68] and projective methods for systems with multiscales [34, 35], HMM also provides a methodology for designing new methods for a large variety of multiscale problems. A framework is presented for the analysis of the stability and accuracy of HMM.
AB - The heterogeneous multiscale method (HMM) is presented as a general methodology for the efficient numerical computation of problems with multiscales and multiphysics on multigrids. Both variational and dynamic problems are considered. The method relies on an efficient coupling between the macroscopic and microscopic models. In cases when the macroscopic model is not explicitly available or invalid, the microscopic solver is used to supply the necessary data for the macroscopic model. Scale separation can be exploited to considerably reduce the complexity of the microscopic solver. Besides unifying several existing multiscale methods such as the ab initio molecular dynamics [13], quasicontinuum methods [73, 69, 68] and projective methods for systems with multiscales [34, 35], HMM also provides a methodology for designing new methods for a large variety of multiscale problems. A framework is presented for the analysis of the stability and accuracy of HMM.
UR - http://www.scopus.com/inward/record.url?scp=85128805678&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85128805678&partnerID=8YFLogxK
U2 - 10.4310/CMS.2003.v1.n1.a8
DO - 10.4310/CMS.2003.v1.n1.a8
M3 - Article
AN - SCOPUS:85128805678
SN - 1539-6746
VL - 1
SP - 87
EP - 132
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 1
ER -