Métodos Computacionais para Problemas Singulares
Computational Methods for Singular Problems
POCTI/MAT/45700/2002
(Project supported by Fundação
para a Ciência e Tecnologia)
Principal
Research Unity: Centro de Matemática e Aplicações
Research Team:
Pedro Lima (Principal Investigator)
Michel Carpentier, Dep. Matemática, Instituto Superior Técnico,
Lisboa (PhD)
Nikolai Chemetov, Dep. Matemática, Faculdade de Ciências,
Universidade de Lisboa (PhD)
Teresa Diogo, Dep. Matemática, Instituto Superior Técnico,
Lisboa (PhD)
António
Oliveira,
Dep. Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de
Lisboa (PhD)
Ricardo Barros,Dep. Matemática,
Faculdade de Ciências e Tecnologia, Universidade de Lisboa (PhD Student)
Madalena Consciência, Dep. Matemática, Faculdade de Ciências,
Universidade de Lisboa (MSc )
Madalena Menezes, Dep. Matemática, Faculdade de Ciências e Tecnologia,
Universidade Nova de Lisboa (PhD Student)
Luisa Morgado, Dep. Matemática, Universidade de Trás-os-Montes e Alto
Douro, Vila Real (PhD Student)
Matilde Pato, Dep.Eng. Química, Instituto Superior de Engenharia de
Lisboa (MSc)
Magda Rebelo, Dep. Matemática, Faculdade de Ciências e Tecnologia,
Universidade Nova de Lisboa (PhD Student)
Filomena Teodoro, Dep. Matemática, Instituto Politécnico de
Setúbal (PhD Student)
Svilen Valtchev, Dep. Matemática, Instituto Superior Técnico, Lisboa
(PhD Student)
Objectives of the project
The main objective of the
present project is to develop new efficient methods for the solution of
mathematical problems which have singularities and cannot be solved by
means of classical methods. The mathematical models that we shall consider
arise in such fields as fluid mechanics, heat conduction and wave propagation.
The investigation of these models leads to boundary value problems for
nonlinear differential equations and Volterra integral equations. The project
has two components: 1) the theoretical investigation of the considered
mathematical models and 2) the development of numerical methods and creation of
computer algorithms for the numerical solution of the problems. The main
characteristic of the methods to be introduced is that they take into
account the asymptotic behavior of the solutions near the singularities. In the
field of Volterra integral equations, we intend to improve the efficency
of the known algorithms for integral equations by introducing such techniques
as variable transformations and graded meshes.
References: Article 1 Article 2 Article 3 Article 4 Article 5
Starting date: September 1st 2003
Activities
2003-2004
P.M.Lima
participated in the XXIV Iberian Latin-American Congress on Computational
Methods in Engineering (CILAMCE 24),29-31 October 2003,
N.
B. Konyukhova, from the Computing Center of Russian
P.M.Lima
and T.Diogo participated in the Ninth International Conference on Enhancement
and Promotion of Computational Methods in Engineering and Science (EPMESC IX),
25-28 November 2003,
T.Diogo
visited Prof. Tao Tang, at Mathematics department of the Baptist University of
Hong Kong, 19 November-4 December 2003.
Prof.
A.I.Sukov, from the
P.M.Lima
visited Prof. Neville Ford at Mathematics department of the
P.M.
Lima and S.Valtchev participated in the congress “Métodos Computacionais em Engenharia”,
held in
P.M.
Lima participated in the International Congress on Computational and Applied
Mathematics (ICCAM 2004), held in Leuven (
2004-2005
P.M.
Lima and N.V. Chemetov participated in the VI International Congress on
Mathematical Modelling, held in Nizhny Novgorod (
The
International Workshop on
Analysis and Numerical Approximation of Singular Problems (IWANASP) took
place at IST, on November 10-12th 2004. The Organizing
Committee was composed by P. M. Lima, M.T. Diogo, N.V. Chemetov and A .
Oliveira. The conference was attended by about 40 persons from 10
countries.
M.
Rebelo, L. Morgado and S.Valtchev presented communications at
IWANASP.
Prof.
N. J Ford visited the Mathematics Department of IST, from January 30th
to February 4th 2005.
The
MSc Thesis of M. Consciência, entitled “Formação de bolhas num
fluido””, was discussed and approved on April 11 , at the Faculdade
de Ciências of the of the University of Lisbon.
Prof.
U. Steffanelli has visited the Faculdade de Ciências of the
M.T.
Diogo and P.M. Lima participated in the XXI Biennial Conference on
Numerical Analysis , held in Dundee (
P.M.
Lima and L. Morgado participated in the conference Equadiff 11,
held in
M.T.
Diogo and M. Rebelo participated in the 7th Hellenic European
Conference on Computer Mathematics and its Applications (Hercma 20005) , held in
2005-2006
Prof. V. Goncharov (Universidade de Évora) visited Prof.
N. Chemetov at Faculdade de Ciências da Universidade de Lisboa on October
2005.
M.T.Diogo
and P.M. Lima visited the
M.T.
Diogo delivered the invited talk “Convergence
Properties of Collocation Methods for a Volterra Integral Equation with
Weakly Singular Kernel” at the seminar of the
M.T.
Diogo and P.M. Lima presented invited communications in the II
International Conference on Scientific Computing and Partial Differential
Equations (SCPDE 05),
held in Hong Kong , December 12-16 2005.
Prof. S. Antontsev (Universidade da Beira Interior)
visited Prof. N. Chemetov in Faculdade de Ciências da Universidade de
Lisboa in January 2006.
Prof,
Neville J. Ford (
Prof.
F. Sadyrbaev (
Prof.
Neville J. Ford (
M. Rebelo and L.Morgado participated and
presented communications in the “Encontro Nacional da Sociedade Portuguesa de
Matemática” (ENSPM06), Instituto Superior
de Engenharia de Lisboa, June 20-23 2006.
T.
Diogo participated and presented a communication at the Twelfth International
Congress on Computational and Applied Mathematics (ICCAM 2006), at the Catholic University
of Leuven (
T.
Diogo and P. Lima participated as organizers at the Second International
Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP06),
held in Samos (
L.
Morgado and M. Rebelo presented communications at the Second International
Workshop on Analysis and Numerical Approximation of Singular Problems (IWANASP06),
held in Samos (
T.
Diogo and P. Lima participated and presented communications at the XXIX Congresso Nacional de Matemática Aplicada e
Computacional (CNMAC),
2006-March 2007 (extension)
P. Lima participated and presented
communication in the 4th WSEAS
International Conference on Fluid Mechanics, Gold Coast (
Prof. A. Pedas (
Prof. A.I. Sukov (
·
O. Antontsev and N. Chemetov, Flux of superconducting
vortices through a domain, SIAM
Journal on Mathematical Analysis, 39
(2006) p. 263-280.
·
N.Chemetov and M. Marques, Non-convex
quasi-variational differential inclusions, submitted.