Mailing Address:

University of California - Davis
Mathematics Department
One Shields Ave
Davis, CA 95616


MSB 2123


BertoMartinez [at]

A good decision is based on knowledge and not on numbers.

– Plato


My research area is a combination of mathematics and computer science. The problem I am concerned with is Material Interface Reconstruction (MIR). The goal of the problem is to approximate the interface separating materials within a given space. More specifically my research is in regards to volume-of-fluid (VOF) methods as an approach to solving MIR problems.

Volume-of-fluid methods work on a domain which is partitioned into a grid. For each cell in the grid the volume fractions of the materials are given. The material fraction of a given material within a cell is defined as the percentage of the cell which is occupied by the given material. In an n-material problem each cell has an associated n-tuple where the ith entry is the percentage of material i present in the given cell. The interface reconstruction is then obtained by using these and only these volume fractions as information.

VOF methods naturally lend themselves to conservation of mass of each material and do not require previous state knowledge to make changes in global topology of the interface.

R. Martinez.  A Survey of Volume-of-Fluid Methods for Material Boundary Reconstruction. Masters, University of California - Davis, —2010—.

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University of California, Davis - Present

Davis, California

Ph.D. - Applied Mathematics

University of California, Davis - 2010

Davis, California

M.S. - Applied Mathematics

Loyola Marymount University - 2005

Los Angeles, California

B.S. - Applied Mathematics
B.S. - Computer Science

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