Computational Mathematics and Applications
The group aims at developing new techniques of mathematical modelling, mathematical analysis, and numerical algorithms for solving problems in applied areas. Currently, group members lead or are involved in multidisciplinary research projects and proposals covering a large domain of disciplinary such as Robotics, Biology, Physiscs and engineering applications. The mathematical analysis not only becomes the basis for defining the mathematical model, but is also essential to understand the properties of the model itself (e.g., the sensitivity to input data). Many of the above mentioned applications do require efficient numerical methods to determine relevant approximations of the solution. The numerical linear algebra is an essential tool in simulation and a part of the goup is dedicated on the design and analysis of algorithms for the computation of eigenvalues and singular values of large matrices, verys much in the spirit of the LAPACK and ScaLAPACK libraries. In general, mathematical models are governed by partial and ordinary differential equations and several teams of the group developing new numerical techniques based on the finite volume methods to provided accurate approximations of the complex and multi-physical problems.
Specific lines of research of members of our group, in collaboration with colleagues from mathematics and applied areas, are:
- Numerical analysis of EDPs, mathematical modelling and scientific computing
- Dynamic Neural Field theory and its application in neuroscience and cognitive robotics
- Water use optimization in irrigation problems
- Approximate solutions for piezoelectric problems for beams.
- Algorithms for structured matrices arising on digital image processing
- The tridiagonal eigenproblem
- The Jordan normal form factorization
- Evaluation of an interior point filter line search method for solving nonlinear optimization problems
- Spectral Computations and Integral Operator Equations
- Finite volume method, high-order approximation, numerical fluid mechanics
- Assessment of spatial correlations in a system of polarizable particles by measuring its optical response.