TY - JOUR
T1 - Diffuse interface energies capturing the Euler number
T2 - Relaxation and renomalization
AU - Du, Qiang
AU - Liu, Chun
AU - Ryham, Rolf
AU - Wang, Xiaoqiang
PY - 2007
Y1 - 2007
N2 - We introduce a set of new interfacial energies for approximating the Euler number of level surfaces in the phase field (diffuse-interface) representation. These new formulae have simpler forms than those studied earlier in [Q. Du, C. Liu and X. Wang, Retrieving topological information for phase field models, SIAM J. Appl. Math., 65, 1913-1932, 2005], and do not contain higher order derivatives of the phase field function. Theoretical justifications are provided via formal asymptotic analysis, and practical validations are performed through numerical experiments. Relaxation and renormalization schemes are also developed to improve the robustness of the new energy functionals.
AB - We introduce a set of new interfacial energies for approximating the Euler number of level surfaces in the phase field (diffuse-interface) representation. These new formulae have simpler forms than those studied earlier in [Q. Du, C. Liu and X. Wang, Retrieving topological information for phase field models, SIAM J. Appl. Math., 65, 1913-1932, 2005], and do not contain higher order derivatives of the phase field function. Theoretical justifications are provided via formal asymptotic analysis, and practical validations are performed through numerical experiments. Relaxation and renormalization schemes are also developed to improve the robustness of the new energy functionals.
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U2 - 10.4310/CMS.2007.v5.n1.a10
DO - 10.4310/CMS.2007.v5.n1.a10
M3 - Article
AN - SCOPUS:34248379040
SN - 1539-6746
VL - 5
SP - 233
EP - 242
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 1
ER -