Lars Viklund

High-level mathematical modeling and programming

Scientific computing and advanced mechanical analysis demand high-level support for modeling and solving complex equations. To meet this need, the authors designed ObjectMath and applied it to real problems in machine-element analysis. >

ObjectMath—an object-oriented language and environment for symbolic and numerical processing in scientific computing

ObjectMath is a language for scientific computing that integrates object-oriented constructs with features for symbolic and numerical computation. Using ObjectMath, complex mathematical models may be implemented in a natural way. The ObjectMath programming environment provides tools for generating efficient numerical code from such models. Symbolic computation is used to rewrite and simplify equations before code is generated. One novelty of the ObjectMath approach is that it provides a comman language and an integrated environment for this kind of mixed symbolic/numerical computation. The motivation for this work is the current low-level state of the art in programming for scientific computing. Much numerical software is still being developed the traditional way in Fortran. This is especially true in application areas such as machine elements analysis, where complex nonlinear problems are the norm. We believe that tools like ObjectMath can increase productivity and quality, thus enabling users to solve problems that are too complex to handle with traditional tools.

The Implementation of ObjectMath - a High-Level Programming Environment for Scientific Computing

We present the design and implementation of ObjectMath, a language and environment for high-level equation-based modeling and analysis in scientific computing. The ObjectMath language integrates object-oriented modeling with mathematical language features that make it possible to express mathematics in a natural and consistent way. The implemented programming environment includes a graphical browser for visualizing and editing inheritance hierarchies, an application oriented editor for editing ObjectMath equations and formulae, a computer algebra system for doing symbolic computations, support for generation of numerical code from equations, and routines for graphical presentation. This programming environment has been successfully used in modeling and analyzing two different problems from the application domain of machine element analysis in an industrial environment

Variant Handling, Inheritance and Composition in the ObjectMath Computer Algebra Environment

ObjectMath is a high-level programming environment and modeling language for scientific computing which supports variants and graphical browsing in the environment and integrates object-oriented constructs such as classes and single and multiple inheritance within a computer algebra language. In addition, composition of objects using the part-of relation and support for solution of systems of equations is provided. This environment is currently being used for industrial applications in scientific computing. The ObjectMath environment is designed to handle realistic problems. This is achieved by allowing the user to specify transformations and simplifications of formulae in the model, in order to arrive at a representation which is efficiently solvable. When necessary, equations can be transformed to C++ code for efficient numerical solution. The re-use of equations through inheritance in general reduces models by a factor of two to three, compared to a direct representation in the Mathematica computer algebra language. Also, we found that multiple inheritance from orthogonal classes facilitates re-use and maintenance of application models.

Object-oriented mathematical modelling—Applied to machine elements

Machine element analysis has a goal of describing function and other aspects of machine elements in a theoretical form. This paper shows how ideas from object-oriented modelling can be applied to machine element analysis. The models thus obtained are both easier to understand, better structured, and allow a higher degree of re-use than conventional models. An object-oriented model description is natural and suitable for machine element analysis. As a realistic example an equational model of rolling bearings is presented. The structure of the model is general, and applies to many types of rolling bearings. The model and one solution require approximately 200 + 200 equations. The model is extensible, e.g. simple submodels of detailed properties can be made more complex without altering the overall structure. The example model has been implemented in a language of our own design, ObjectMath (Object-oriented Mathematical language for scientific computing). Using ObjectMath, it is possible to model classes of equation objects, to support multiple and single inheritance of equations, to support composition of equations, and to solve systems of equations. Algebraic transformations can conveniently be done since ObjectMath models are translated into the Mathematica computer algebra language. When necessary, equations can be transformed to C++ code for efficient numerical solution. The re-use of equations through inheritance reduced the size of the model by a factor of two, compared to a direct representation of the model in the Mathematica computer algebra language.

An object-oriented language for symbolic computation—applied to machine element analysis

In this paper we present the ObjectMath language, a hybrid language integrating object-oriented constructs with features for symbolic and numeric computation. Complex mathematical models may be implemented in a natural way using ObjectMath. Objects are used to structure models that might consist of a large number of equations while inheritance facilitates reuse of equations and formulae. The class specialization hierarchy is also used to generate spxialized efficient numeric code from general symbolic equations and expressions. A first prototype of the ObjectMath programming environment has bean implemented and successfully used for modeling and analyzing two different machine element analysis problems.