Classical Numerical Methods in Scientific Computing

Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the...

Down-Hole Electromagnetic Heating of Deep Aquifers for Renewable Energy Storage

Electromagnetic (EM) heating is an emerging method for storing renewable energy, such as photovoltaic solar and wind electric power, into aquifers. We investigate how the captured energy increases the temperature of a prototypical deep aquifer for a six-month period and then to which extent the stored energy can be recovered during the...

Review and perspectives in quantum computing for partial differential equations in structural mechanics

Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods is required to find approximate solutions. However, for many problems of practical interest, the computational cost of classical numerical solvers running on...

Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations in computational fluid dynamics problems. This preconditioning technique exploits the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to...

Evaluation of Multilevel Sequentially Semiseparable Preconditioners on CFD Benchmark Problems Using IFISS

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU...

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...

Comparison of boundary layer calculations for the root section of a wing

At the workshop nine participants presented the results of their calculations for a practical test case. The test case deals with the 3D turbulent boundary layer development, including separation, on the root section of a swept wing. The employed calculation methods comprise 3D integral methods as well as field methods. A short description of...