Boundary element method for a free third boundary problem modeling tumor growth with spectral accuracy. (English) Zbl 1458.92023
Summary: By boundary element method, we present a numerical iterative process for solving a free third boundary problem modeling tumor growth with spectral accuracy. The piecewise quadratic curves are fitted to maintain local smoothness of the boundary at every node. The double-layer and single-layer potentials with weakly singular kernels are evaluated with spectral accuracy. The method of characteristics is employed to transform interfacial velocity PDE into discrete ODEs. The numerical integral formula for weakly singular operator with logarithmic singularity is deduced and the convergence and error are presented. The nonradially symmetric solutions of the free boundary problem on a perturbed boundary are provided to test the accuracy and effectiveness of the numerical method.
MSC:
| 92C32 | Pathology, pathophysiology |
| 65M38 | Boundary element methods for initial value and initial-boundary value problems involving PDEs |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
double-layer and single-layer potentials; characteristic curve; weakly singular kernel; spectral accuracyReferences:
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