2013/04/01 by David Kapanadze, Kapanadze, David, Gennady Mishuris +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #30E25 #33E05 #35B27 #74Q05 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in engineering #Numerical methods in inverse problems #math-ph #math.MP #msc:30E25 #msc:33E05 #msc:35B27 #msc:74Q05
paper · pdf · doi:10.48550/arxiv.1304.0388
23 pages, 10 figures
openalex publication_date 2013/04/01 · arxiv created 2013/08/25 · arxiv updated 2013/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a boundary value problem in unbounded 2D doubly periodic composite with circular inclusions having arbitrary constant conductivities. By introducing complex potentials, the boundary value problem for the Laplace equation is transformed to a special R-linear BVP for doubly periodic analytic functions. This problem is solved with use of the method of functional equations. The R-linear BVP is transformed to a system of functional equations. A new improved algorithm for solution of the system is proposed. It allows one not only to compute the average property but to reconstruct the solution components (temperature and flux) at an arbitrary point of the composite. Several computational examples are discussed in details demonstrating high efficiency of the method. Indirect estimate of the algorithm accuracy has been also provided.