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Activity Funded

Center for Computational and Stochastic Mathematics

Centro de Matemática Computacional e Estocástica

Reference
UID/04621/2025
Project Start Date
2025-01-01
Project End Date
2029-12-31
Principal Investigator
Funding Program
Avaliação UID 2023/2024

Abstract

CEMAT is a R&D Unit of IST-ID, ULisboa, devoted to high quality interdisciplinary research, innovation, and advanced education in computational and stochastic mathematics with focus on sciences and engineering applications, and to an active cooperation with industries. In 2025-2029, the research activities will be directed to reinforce the areas where the team is internationally recognized, namely: Algebra and Computing, Applied and Numerical Analysis, Mathematical Modeling in Biomedicine, and Statistics and Stochastic Processes. The objective is to deepen current research themes of identified significance and to extend the knowledge to new emergent interdisciplinary topics. The research plan in each of the research areas is the following: ALGEBRA AND COMPUTING: Research will be devoted to two major areas. Algebra and applications: although focusing on the classical algebraic structures on which the team members have consolidated their expertise, the group plans to address some questions on applications of algebra. Computing: the main topics deal with the development of computational tools for the research in mathematics and in algebra, making possible or easier to obtain new results. APPLIED AND NUMERICAL ANALYSIS: Research will focus on meshfree methods for PDEs, namely, coupling the Method of Fundamental Solutions (MFS) with domain decompositions, techniques for particular solutions, and applications to non-linear PDEs; iterative meshfree techniques and continuous/discontinuous FEM for Navier-Stokes equations and related models; analysis and control of fluid models with open boundary conditions; new algorithms for generalized integral and differential equations describing the dynamics of infectious diseases, modeling of anomalous diffusion and complex viscoelasticity, and neural field models; Industrial Mathematics problems. MATHEMATICAL MODELING IN BIOMEDICINE: Research will be focused on the mathematical modeling and numerical simulation of complex biophysical systems associated to highly relevant problems in biomedicine, namely in cardiovascular modeling, and in mathematical biology. These studies use sophisticated multiscale mathematical models highly integrated with efficient algorithms, to increase understanding and control of those complex systems. STATISTICS AND STOCHASTIC PROCESSES: As a result of current collaborations, and considering the 2030 Agenda – Sustainable Development Goals, members of the group have projects to participate in the development of statistical techniques within the scope of investments in renewable energy and to develop user-friendly tools for on-field soil health assessment. It is also intended to create a new area of research in statistical models for 3D point cloud data. In addition to these new topics, members will continue fundamental and applied research in multivariate analysis, quality control, robust statistics, queueing processes, stochastic optimization, time series and extreme value theory.

Institutions

Main Institutions

  • Universidade de Lisboa Centro de Matemática Computacional e Estocástica (ULisboa CEMAT)
  • Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento (IST-ID)

Funding 485.957,48 €

Fundação para a Ciência e a Tecnologia (FCT) - Portugal

485.957,48 €