Three different approaches for the determination of conservation laws of differential equations are presented. For three corresponding REDUCE computer algebra programs CONLAW1/2/3 the necessary subroutines are described. One of them simplifies general solutions of overdetermined PDE systems so that all remaining free functions and constants correspond to independent conservation laws. It determ...

Abaqus is often applied to solve geomechanical boundary value problems. Several Abaqus built-in features enable a wide range of simulating such problems. For complex problems Abaqus can be extended via user subroutines. Several extensions for soil mechanics purposes are discussed and corresponding case studies are presented.

A new accelerated algorithm to solve the single-facility minisum location problem is developed. The acceleration is achieved using a feedback factor. The proposed algorithm converges faster than the accelerating procedures available in the literature. Being nearly as simple as the classical Weiszfeld procedure, the new method can easily be implemented in real applications. Practical subroutines...

This paper discusses analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory, representation theory, and statistics. Our methods are based on the study of rational functions with poles on arrangements of hyperplanes; they surpass traditional exhaustive enumeration and can even yield formulas when the input data con...

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from saddles one has to use second-order methods. However, most works on second-order methods rely extensively on expensive Hessian-based computations, making them ...

A system of PL/I procedures has been written that permits geometric objects to be described hierarchically. The objects are themselves represented as P L / I procedures, allowing very general use of variables. By effectively intercepting subprogram calls, the system provides a means of modifying the semantics associated with any object without modifying the object’s procedural description