Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

Constraint reasoning for differential models

The basic motivation of this work was the integration of biophysical models within the interval constraints framework for decision support. Comparing the major features of biophysical models with the expressive power of the existing interval constraints framework, it was clear that the most important inadequacy was related with the representation of differential equations. System dynamics is often modelled through differential equations but there was no way of expressing a differential equation as a constraint and integrate it within the constraints framework. Consequently, the goal of this work is focussed on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the new formalism of Constraint Satisfaction Differential Problems. Such framework allows the specification of ordinary differential equations, together with related information, by means of constraints, and provides efficient propagation techniques for pruning the domains of their variables. This enabled the integration of all such information in a single constraint whose variables may subsequently be used in other constraints of the model. The specific method used for pruning its variable domains can then be combined with the pruning methods associated with the other constraints in an overall propagation algorithm for reducing the bounds of all model variables. The application of the constraint propagation algorithm for pruning the variable domains, that is, the enforcement of local-consistency, turned out to be insufficient to support decision in practical problems that include differential equations. The domain pruning achieved is not, in general, sufficient to allow safe decisions and the main reason derives from the non-linearity of the differential equations. Consequently, a complementary goal of this work proposes a new strong consistency criterion, Global Hull-consistency, particularly suited to decision support with differential models, by presenting an adequate trade-of between domain pruning and computational effort. Several alternative algorithms are proposed for enforcing Global Hull-consistency and, due to their complexity, an effort was made to provide implementations able to supply any-time pruning results. Since the consistency criterion is dependent on the existence of canonical solutions, it is proposed a local search approach that can be integrated with constraint propagation in continuous domains and, in particular, with the enforcing algorithms for anticipating the finding of canonical solutions. The last goal of this work is the validation of the approach as an important contribution for the integration of biophysical models within decision support. Consequently, a prototype application that integrated all the proposed extensions to the interval constraints framework is developed and used for solving problems in different biophysical domains.

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

POST-PROCESSING TECHNIQUES SUITABILITY FOR MESOLEVEL FREE BOUNDARY FLOWS

Reliable flow simulation software is inevitable to determine an optimal injection strategy in Liquid Composite Molding processes. Several methodologies can be implemented into standard software in order to reduce CPU time. Post-processing techniques might be one of them. Post-processing a finite element solution is a well-known procedure, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Post-processing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. In previous works influence of smoothness of non-homogeneous Dirichlet condition, imposed on smooth front was examined. However, usually quite a non-smooth boundary is obtained at each time step of the infiltration process due to discretization. Then direct application of post-processing techniques does not improve final results as expected. The new contribution of this paper lies in improvement of the standard methodology. Improved results clearly show that the recalculated flow front is closer to the ”exact” one, is smoother that the previous one and it improves local disturbances of the “exact” solution.

Post-processing Techniques in Free Boundary Flows during Liquid Composite Moulding Processes

Post-processing a finite element solution is a well-known technique, which consists in a recalculation of the originally obtained quantities such that the rate of convergence increases without the need for expensive remeshing techniques. Postprocessing is especially effective in problems where better accuracy is required for derivatives of nodal variables in regions where Dirichlet essential boundary condition is imposed strongly. Consequently such an approach can be exceptionally good in modelling of resin infiltration under quasi steady-state assumption by remeshing techniques and with explicit time integration, because only the free-front normal velocities are necessary to advance the resin front to the next position. The new contribution is the post-processing analysis and implementation of the freeboundary velocities of mesolevel infiltration analysis. Such implementation ensures better accuracy on even coarser meshes, which in consequence reduces the computational time also by the possibility of employing larger time steps.

On the HHT, its problems, and some solutions

Mechanical Systems and Signal Processing, Vol.22, Number 6

Pseudo-fractional ARMA modelling using a double Levinson recursion

IET Control Theory & Applications, Vol. 1, Nº 1

The Serravallian-Tortonian boundary in the lower Tagus Basin (Portugal) and the new GSSP of the Tortonian stage

Revista electrónica de Ciências da Terra,http://e-terra.geopor.pt,Geociences on-line journal, Vol. 6, nº1

New insights into pseudo-fractional ARMA modelling

Proceedings of the International Conference on Computational Cybernetics, Vienna University of Technology, August 30 - September 1, 2004

MASS CONSERVATION ENHANCEMENT OF FREE BOUNDARY FLOWS IN COMPOSITES MANUFACTURING

Undesirable void formation during the injection phase of the liquid composite molding process can be understood as a consequence of the non-uniformity of the flow front progression, caused by the dual porosity of the fiber perform. Therefore the best examination of the void formation physics can be provided by a mesolevel analysis, where the characteristic dimension is given by the fiber tow diameter. In mesolevel analysis, liquid impregnation along two different scales; inside fiber tows and within the spaces between them; must be considered and the coupling between these flow regimes must be addressed. In such case, it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. When continues Galerkin method is used, exploiting elements with velocity components and pressure as nodal variables, strong numerical implementation of such boundary conditions leads to ill-posing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. This article presents a numerical procedure, which was formulated and implemented in the existing Free Boundary Program in order to significantly reduce this error.

Mass Conservation Enhancement of Free Boundary Mesolevel Flows during LCM Processes of Composites Manufacturing

Undesirable void formation during the injection phase of the liquid composite moulding process can be understood as a consequence of the non-uniformity of the flow front progression, caused by the dual porosity of the fibre perform. Therefore the best examination of the void formation physics can be provided by a mesolevel analysis, where the characteristic dimension is given by the fibre tow diameter. In mesolevel analysis, liquid impregnation along two different scales; inside fibre tows and within the open spaces between them; must be considered and the coupling between these flow regimes must be addressed. In such case, it is extremely important to account correctly for the surface tension effects, which can be modelled as capillary pressure applied at the flow front. Numerical implementation of such boundary conditions leads to ill-posing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. This contribution presents a numerical procedure, which was formulated and implemented in the existing Free Boundary Program in order to significantly reduce this error.

The Transversarium-Bifurcatus Zone boundary at Rocha (Peral area, East-Central Algarve, Portugal)

This paper represents the first detailed study of the Transversarium-Bifurcatus Zone boundary in the Algarve. The boundary studied in the Peral area is associated with a stratigraphic discontinuity, whose hiatus partially affects the Transversarium-Bifurcatus Zones. A discontinuity was also recognized in the Bifurcatus-Birnammatum Zone boundary, which can be correlated with the traces of a Type II unconformity, which separates cycles 4.3-4.4 in HAQ et al. (1987), present on the South Iberian palaeomargin. An analysis was made of the ecostratigraphic evolution in the interval between the uppermost Transversarium Zone and the lower part of the Bimammatum Zone on the basis of the faunal spectra obtained. We conclude that ammonites are the most tolerant cephalopods to the ecological stress caused by the increase of inflows and the decrease of the shelf's ecospace. Benthic fauna decreased considerably in these conditions. A relatively abundant and diversified fauna ofDichotomoceras is noteworthy among the ammonites collected, as this genus was previously little known in the Algarve.

Ostracodes; witnesses of the Plio-Quaternary boundary in the North Eastern Atlantic preliminary results

Proceedings of the 1" R.C.A.N.S. Congress, Lisboa, October 1992

Pliensbachian/Toarcian boundary: the proposed GSSP of Peniche (Portugal)

The Peniche section (Portugal) is considered as a potential stratotype (GSSP) for the Pliensbachian/Toarcian boundary and it is analysed on the background of the available data on the ammonite successions from other Tethyan and NW European areas.

Calcareous nannofossil assemblages around the Pliensbachian/Toarcian boundary in the reference section of Peniche (Portugal)

The Pliensbachian/Toarcian boundary (Lower Jurassic) is well represented in the Lusitanian Basin (Portugal), mainly in the Peniche area, recorded by a marl/limestone series. Calcareous nannofossil assemblages are described herein, with the aim to contribute to the Toarcian GSSP definition. Marly samples were collected 3 m below and 7 m above this boundary and analysed for calcareous nannofossils. The main nannofossils observed were Biscutum finchii, B. grande, Calcivascularis jansae, Crepidolithus crassus, C. granulatus, C. impontus, Lotharingius hauffii, L. sigillatus, L. aff. L. velatus, Schizosphaerella spp. and Tubirhabdus patulus. This assemblage indicates that the Pliensbachian/Toarcian boundary in Peniche lies in the upper part of the NJ5b Subzone. Schizosphaerella and Lotharingius dominate the assemblage. The abundant occurrence of C. jansae and the common occurrence of B. grande indicate a strong Tethyan influence.