Activity Group leaders:
Computation has joined theory and experiment as a primary method of scientific discovery. Advances in computer hardware and software environments have dramatically increased the size and complexity of models and data sets that can be feasibly studied. Nowadays, computer models are routinely used to study phenomena that cannot be studied using laboratory experiments (e.g., galaxy formation, protein folding, tsunamis, risk in financial markets, global climate change, etc.).
Computer models are also used in industry to reduce product-development cycles by enhancing or even replacing construction of prototypes (e.g., in aerospace, materials design and synthesis, energy generation, etc.). Scientific Computing – a vibrant field in Canada’s Applied Mathematics community – is dedicated to filling the growing need for robust algorithms and software in science and industry. The work of researchers in Scientific Computing provides the means to elicit practical insights once deemed unattainable. The principal goals in Scientific Computing are:
- to understand and improve potential numerical procedures that underly computer-based solutions of continuous mathematical problems;
- to build robust and efficient numerical software libraries or problem-solving environments and to analyze and evaluate them critically; and
- to support practitioners of Computational Science in applying mathematical models and software tools to develop reliable simulations for their domain-specific applications.
The foundations of Scientific Computing comprise numerous powerful techniques of mathematical analysis developed during the era of hand and mechanical calculations; Newton, Gauss, Lagrange, and Euler (among many other well-known mathematicians) contributed many fundamental concepts and algorithms. Then, as now, realistic models for practical science and engineering typically involved mathematically formulated problems – in particular, algebraic, transcendental, and differential equations – that can be solved only using numerical approximations.