Research work in Acoustic and Elastic
Scattering which
has been carried out by us in the last
years consists mainly
in non-destructive obstacle detection.
The direct problem consists in (knowing
the incident waves
and the shape of the obstacle) determining
the scattered wave.
Here, research work was focused in applying
the Boundary
Finite Element Method to calculate the
elastic scattered wave
produced by one or more plane cracks.
The far-field patterns
and the scattering cross sections obtained
showed some
advantages of this method.
Associated to this subject is the calculation
of the resonance
frequencies. We have determined the complex
resonance
frequencies for some cracks and studied
the relation with the
scattering cross section peaks.
The trapping case was also considered.
The inverse obstacle problem consists
in (knowing the incident
waves and the scattered wave) determining
the shape of the
obstacle. Research work in this area was
mainly focused in
developping numerical schemes and uniqueness/characterization
theorems.
Research in detection of defects on materials,
like cracks or
inhomogeneities in a bounded domain is
being carried also.
Obs: The picture show the far field pattern produced
by elastic waves scattered by a crack.
Alves C. J. S., Ben Abdallah J., Jaoua M. : "Recovery of cracks using a reciprocity gap function", accepted for publication in Inverse Problems in Engineering Alves, C. J. S., El Badia A., Ha Duong T. : "On the determination of elastic point sources", accepted for publication in the PICOF'02 proceedings. Alves C. J. S., Chen C. S., Sarler B. : "The method of fundamental solutions for solving Poisson's problems"; accepted for publication in the BEM XXIV proceedings. Alves C. J. S., Pereira B., Serranho P. : "Scattering by cracks: Numerical simulations using a boundary finite element method", accepted for publication in the BEM XXIV proceedings. Alves C. J. S., Kress R. : "On the far field operator in elastic obstacle scattering". IMA J. Appl. Math., 67,1-21 (2002). Alves C. J. S.,Ammari H.. : "Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium". SIAM J. Appl. Math., 62, pp.94-106. (2001) Alves C. J. S.,Chen C. S. : The method of fundamental solutions adapted for a non homogeneous equation", in the Proceedings of the International Conference in Engineering & Science 2001 (ICES'01). Tech Science Press in CD-ROM. (2001) Alves C. J. S. : "Numerical experiments on the near and far field of acoustic and elastic waves scattered by cracks", in the Proceedings of the International Conference in Engineering & Science 2001 (ICES'01). Tech Science Press in CD-ROM. Alves C. J. S., Ha Duong T., Penzel F. : "On the identification of conductive cracks", in Inverse Problems in Engineering Mechanics II (Editors: M. Tanaka and G. Dulikravich). Elsevier Publ., pp.213-218 (2000). Alves C. J. S., Pires G. E. : "Sound soft screen detection in the near field", in Inverse Problems in Engineering Mechanics II (Editors: M. Tanaka and G. Dulikravich). Elsevier Publ., pp.563-571 (2000). Alves C. J. S. : "Density results for the Helmholtz equation and the method of fundamental solutions", in Advances in Computational Engineering & Sciences - Volume I (Editors: S. N. Atluri and F. W. Brust). Tech Sc. Press, pp.45-50 (2000) Alves C. J. S. : "Numerical simulations on resonance poles - the trapping case of two plane cracks". J. Comp. Appl. Math., 111, pp.267-279 (1999) Alves C. J. S., Ha Duong T. : "Inverse scattering for elastic plane cracks". Inverse Problems, 15, pp.91-97 (1999) Alves C. J. S., Ribeiro P. M. C. : "Crack detection using spherical incident waves and near-field measurements", in Boundary Elements XXI (Editors: C. A. Brebbia, H. Power). WIT Press, Southampton, pp.355-364 (1999) Alves C. J. S. : "Inverse scattering with spherical incident waves", in Mathematical and Numerical Aspects of Wave Propagation (Editor: DeSanto, J.). SIAM, pp.502-504 (1998) Alves C. J. S., Ha Duong T. : "On inverse scattering by screens". Inverse Problems, 13, pp.1161-1176 (1997) Alves C. J. S., Ha Duong T. : "On the far field amplitude for elastic waves", in Modern Mathematical Methods in Diffractions Theory and its Applications in Engineering (Editor: E. Meister). Peter Lang, Frankfurt, pp.49--67 (1997) Alves C. J. S., Ha Duong T. : "Numerical resolution of the Boundary Integral Equations for elastic scattering by a plane crack". Int. J. for Num. Meth. in Eng., 38, pp.2347-2371 (1995)
Alves C. J. S., Ha Duong T. : "Numerical experiments on the resonance poles associated to acoustic and elastic scattering by a plane crack", in Mathematical and Numerical Aspects of Wave Propagation (Editor: Gary Cohen). SIAM, pp. 544-553 (1995)