Automated computational modelling for complicated partial differential equations

In engineering, physical phenomena are often described mathematically by partial differential equations (PDEs), and a commonly used method to solve these equations is the finite element method (FEM). Implementing a solver based on this method for a given PDE in a computer program written in source code can be tedious, time consuming and error...

Automated Solution of Partial Differential Equations with Discontinuities using the Partition of Unity Method

Although computers were invented to automate tedious and error-prone tasks, computer programming is a tedious and error-prone task itself. This is a well-known paradox in the field of computational mathematical modelling. Recently, automatic code generation has been proposed to solve this paradox. In this approach, a required code to model...