Venezuela II:
1978 – 1984

In 1978, I returned to Caracas to my former job at Universidad Central de Venezuela.

Some additional work appeared in:

J. A. Rial

While still at Caltech I had met the Venezuelan seismologist José A. Rial, who was a student at the Seismo Lab. and had had many conversations on basic seismology that were very useful for my education on the subject.

Upon his return to Caracas we started a collaboration that lasted many years and has produced several publications:

In 1980, while visiting Stanford, I met Greg Wojcik and started my long and fruitful relationship with him and the company for which he worked, Weidlinger Associates, first as a Consultant and eventually as a full time employee.

Nan and Greg Wojcik

Other interactions with students and colleagues produced some additional work:

“Smooth Monotone Spline Interpolation”, with G. Pagallo, Lect. Notes Mathematics 909:142-146 (1982)

This early work on shape preserving interpolation was motivated by our interest in producing a practical implementation of the ideas of Andy White on adaptive mesh refinement (analytic changes of variables used in the method needed to be monotonic). My student Omaira Rodriguez used some of these ideas in her Master Thesis, in an early attempt to extend the work to the solution of nonlinear conservation laws.

O. Rodriguez

G. Pagallo

As a result of a contract with the Venezuelan Petroleum Research Institute, INTEVEP, we worked on the solution of large sparse systems arising in Petroleum Reservoir Engineering and wrote:

In 1982 I organized an International Meeting in Caracas that initiated a tradition that continues to the present in various Latin American locations (Brasil, Peru, Argentina, Honduras, Mexico, Venezuela), as the Panamerican Workshops in Applied and Computational Mathematics. Since the event in Argentina, this activity has been enriched with an Advanced Studies Institute (PASI), sponsored by NSF and DOE, under the able stewardship of José Castillo, San Diego State University, and with my close collaboration. In this enlightened program, NSF and DOE provide funds for travel and expenses for the Instructors of eight short courses and 40 students from the Américas.

The final contribution in the PASVA series was:

This contains all the generality required to solve two-point seismic ray tracing problems in heterogeneous, piece-wise smooth media. Oddly enough, one of the first users was C. Wilts at Caltech, who applied it to the solution of Schrodinger equations arising in the modeling of bubble memories.

As the result of a summer visit to the Berkeley Lawrence Laboratory we wrote:

The purpose of this research was to identify the position of liquid meniscus under low gravity and it also used PASVA4 for its solution. A few years later Paul Concus had an experiment carried on the space Shuttle that confirmed this modeling. The interest for NASA was to make sure that the inlets in fuel tanks were positioned properly.

During my 17 years in Venezuela I had the pleasure and the privilege of interacting with many bright students and colleagues, both in Computer Sciences, as well as in Mathematics and Engineering. I helped create the programs in Computer Sciences (with Julián Araoz, Cristina Zoltán, Carlos Domingo, Oscar Varsavsky and Manuel Bemporad among others), and Applied Mathematics (in the Department of Mathematics). I also put on a solid footing the discipline of Scientific Computing that is still today going strong, lead by many of my students that went abroad to get their Ph D’s, and more recently by some of their students.

M. Raydan

P. Concus

Amanda and Julian Araoz