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Efficient Simulation and Computation for Health, Sea and Industry

Problem Description

New efficient numerical tools are developed and applied to three applications: molding process optimization, port protection and retina assessment. Computational efficiency lies on the design of very high-order method that take advantage of today’s hardware capabilities. In this project, we development new Key Enabling Technologies (KET) involving applied mathematics and computer sciences and simulation tools for applications strongly inserted in the national and regional Research and Innovation Strategies for Smart Specialization.

Modelling & Computational Challenges

The demand for modelling intricate systems often involving multiscales and multiphysics around complex geometries has been a source of motivation for great progress in the field of computational mathematics. High-order methods for solving partial differential equations, such as finite element methods or spectral methods, are attractive due to the need of great accuracy on realistic models. Nevertheless, a number of challenges still exist not only in the development of new mathematical tools but also in translating academic progresses into engineering practice. 

Research at LCM

In this project, we propose to develop Discontinuous Galerkin (DG) methods which can be used in a space-time approach, giving an effective framework for high-order accurate methods. In this technique, time is considered as an extra dimension and it is treated in the same way as the spatial coordinates. Space-time DG methods, while allowing for discontinuities in the temporal discretization, combine the well-known advantages of the DG methods, such as of flexibility for local mesh refinement, adjustment of the polynomial order in each element and excellent performance on parallel computers. 

This study will be considered in the framework of a more general project that aims develop a computational model to simulate the electromagnetic wave’s propagation through the eye’s structures to create a virtual optical a virtual optical coherence tomography scan and to model and simulate ocular tissues, focusing on stroma collagen organization, a key factor for eye transparency.

Project Team

      • Stephane Clain (PI), CPhy /DMA, University of Minho 
      • Gaspar Machado, CPhy/DMA, University of Minho
      • Ricardo Costa, IPC, University of Minho 
      • Alberto Proenca, ALGORITM, University of Minho 
      • Rui Pereira, DMA, University of Minho 
      • Jorge Figueiredo, CPhy /DMA, University of Minho 
      • João Nóbrega, DPE, University of Minho 
      • Olga Carneiro, IPC, University of Minho
      • Cláudia Reis, CERIS,, IST,  University of Lisbon 
      • Maria Ana Baptista, IDL, University of Lisbon 
      • Adérito Luís Martins Araújo, CMUC, University of Coimbra
      • António Miguel Morgado, DPhy, University of Coimbra 
      • Sílvia Barbeiro, CMUC, University of Coimbra
      • Rui Bernardes, CIBIT/iCBR, University of Coimbra 

      Project Reference