Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials

Numerical Algorithms

Volumn 43, Issue 4, 2006, Pages 309-330

  Rutka, Vita ^a   Wiegmann, Andreas ^b  

^a UNIVERSITY OF KONSTANZ   (Germany)

^b FRAUNHOFER INSTITUTE FOR INDUSTRIAL MATHEMATICS ITWM   (Germany)

Author keywords

Composite materials; Effective elastic moduli; Explicit jump immersed interface method; Linear elasticity; Virtual material design

Indexed keywords

EID: 33847422210     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-007-9063-9     Document Type: Article

References (13)

1. Aboudi, J.: Mechanics of Composite Materials. Elsevier, Amsterdam, The Netherlands (1991)
2. Allaire, G.: Shape Optimization by the Homogenization Method. Springer, Berlin Heidelberg New York (2002)
3. LeVeque, R.J., Li, Z.: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31, 1019-1044 (1994)
4. Li, Z.: A fast iterative algorithm for elliptic interface problems. SIAM J. Numer. Anal. 35(1), 230-254 (1998)
5. Mayo, A.: The fast solution of Poisson's and the biharmonic equations on irregular regions. SIAM J. Numer. Anal. 21(2), 285-299 (1984)
6. Osher, S.J., Sethian, J.A.: Fronts propagating with curvature dependent speed: algorithms based on the Hamilton-Jacobi formulation. J. Comput. Phys. 79, 12-49 (1988)
7. Rutka, V.: A fast numerical method for the computation of effective elastic moduli of 3D fibrous microstructures. Master's thesis, University of Kaiserslautern (2001)
8. Rutka, V.: Immersed interface methods for elliptic boundary value problems. Ph.D. thesis, TU Kaiserslautern (2005)
9. Rutka, V., Wiegmann, A., Andrä, H.: EJIIM for calculation of effective elastic moduli in 3D linear elasticity. Technical Report 93, Fraunhofer ITWM Kaiserslautern (2006)
10. Sethian, J.A., Wiegmann, A.: Structural boundary design via level set and explicit jump immersed interface methods. J. Comput. Phys. 163(2), 489-528 (2000)
11. Wiegmann, A.: Fast Poisson, fast Helmholtz and fast linear elastostatic solvers on rectangular parallelepipeds. Technical Report LBNL-43565, Lawrence Berkeley National Laboratory, MS 50A-1148, One Cyclotron Rd, Berkeley CA 94720 (1999)
12. Wiegmann, A., Bube, K.P.: The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions. SIAM J. Numer. Anal. 37(3), 827-862 (2000)
13. Yang, X., Li, B., Li, Z.: The immersed interface method for elasticity problems with interfaces. Dyn. Contin., Discrete Impuls. Syst. 10(5), 783-808 (2003)