Diffuse interface energies capturing the Euler number: Relaxation and renomalization

Qiang Du, Chun Liu, Rolf Ryham, Xiaoqiang Wang

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)233-242
Number of pages10
JournalCommunications in Mathematical Sciences
Issue number1
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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