Boundary element method for a free boundary problem modeling three dimensional tumor growth

In the mathematical model of tumor growth, the initial boundary surface of the three dimensional tumor domain is known, but the tumor domain and its boundary surface change over time in a way that is unknown in advance. People are concerned whether the tumor is likely to spread or shrink and how the tumor will change. In this article, by the boundary element method, the free boundary problem in the three-dimensional tumor domain will be solved via the integration on a two-dimensional boundary surfaces (at the expense of singularity in the Green's functions). We will numerically compute and graphically show the changing boundary surfaces of the three dimensional tumor domain over time. We will numerically analyze the trend of tumor growth with varying proliferation rate μ. Our numerical approach Professor Bei Hu proposed is new and our numerical experiments contribute to the prediction of tumor growth in clinical medicine.