This paper presents a knowledge-based problem solving environment for numerical simulation of problems described by partial differential equations (PDEs). The system aims to facilitate the simulation requirements of different user groups that include engineers, mathematicians and numerical analysts. To attain this objective, a flexible multi-perspective modelling environment is proposed which incorporates three natural modelling platforms, namely; a physical model, a mathematical model and a numerical model. The modelling environment is integrated with a sophisticated numerical solver. We believe that combination of an open modelling system with a basic numerical simulator provides a powerful problem solving environment capable of meeting the needs of these different user groups. The overall system architecture is based on automatic transformation using mathematical and numerical knowledge bases between the three identified models. The knowledge bases are organized in a frame based manner to reflect the hierarchical nature of the knowledge in PDEs and numerical algorithms. The object oriented paradigm is used to bind local rule bases to each frame and for implementing a global inference mechanism which works over the hierarchical knowledge structures. Evaluation of the modelling environment has indicated that engineers can tackle PDE based engineering problems without the necessity for detailed knowledge of mathematics or numerical techniques and mathematicians can examine the mathematical properties of PDEs without the requirement of numerical expertise.
