Numerical Methods and Numerical Analysis Research

Developing advanced computational techniques, mathematical models and simulation tools to solve complex engineering, physical and industrial problems at the University of Lancashire.

Research Overview

Numerical methods research at the University of Lancashire combines mathematics, scientific computing, engineering and physics to develop efficient computational techniques for solving real-world problems. Research spans the development, analysis, implementation and application of numerical algorithms for differential equations, integral equations, inverse problems and engineering simulations.

The University has particular expertise in boundary element methods, computational acoustics, inverse modelling and scientific software development, supporting applications across engineering and applied science.

The LinkedIn Group Numerical Methods has been created to connect the people interested in the numerical mathematics field. You can also link to the LinkedIn profile Numerical Analyst.

The website www.numerical-methods.com has been created to share reources in numerical methods.

Mathematics, Modelling and Computation

Research focuses not only on solving mathematical problems but also on understanding the accuracy, stability, efficiency and reliability of computational algorithms. Numerical analysis provides the theoretical foundation that underpins modern simulation, digital engineering and scientific computing.

Research Themes

Boundary Element Methods (BEM)

Development and analysis of boundary element techniques for acoustic, engineering and physical applications. The LinkedIn Group Boundary Element Method has been created to connect the people interested in boundary elements.

Computational Acoustics

Numerical simulation of sound propagation, aeroacoustics, loudspeaker systems and noise control. The LinkedIn Group Finite Difference Method has been created to connect the people interested in finite difference methods.

Inverse Problems

Recovering unknown physical information from measured data through advanced computational techniques.

Finite Difference Methods

Numerical approaches for solving differential equations arising in engineering and physics. The LinkedIn Group Finite Difference Methods has been created to connect the people interested in finite differences.

Electromagnetic Simulation

Computational modelling using finite-difference time-domain and related numerical techniques. The LinkedIn Group FDTD method in Electromagnetic and Acoustic Simulation has been created to connect the people interested in FDTD method.

Scientific Computing

Design and implementation of efficient algorithms and high-performance computational software.

Engineering and Scientific Applications

Numerical methods developed at the University have been applied to a wide range of industrial and scientific challenges, particularly in acoustics and engineering analysis. Research has included the simulation of acoustic fields, loudspeaker systems, aircraft and engine noise, diffusion processes and electromagnetic devices. :contentReference[oaicite:1]{index=1}

Software and Computational Tools

A distinctive aspect of the University's research is the development of practical computational software implementing advanced numerical methods. Research has produced algorithms, codes and software tools supporting the solution of engineering and acoustics problems using boundary element and related computational techniques. :contentReference[oaicite:2]{index=2}

MATLAB and Scientific Computing

Algorithm development, numerical experimentation and modelling.

Boundary Element Software

Specialist software for acoustic and engineering simulations.

Fortran and High-Performance Computing

Efficient implementations of large-scale numerical algorithms.

Computational Modelling Platforms

Supporting simulation, analysis and engineering design.

Research Environment

Numerical methods research is closely linked to mathematics, acoustics, engineering and physics activities within the University. The work contributes to the wider research strengths of the Jeremiah Horrocks Institute and supports interdisciplinary projects involving aerospace, acoustics, manufacturing and computational science. :contentReference[oaicite:3]{index=3}

Postgraduate Research Opportunities

MSc

Research-focused computational mathematics projects

PhD

Numerical analysis and scientific computing research

Industry

Collaborative engineering and modelling projects

Software

Algorithm and simulation tool development

Research students have opportunities to investigate new numerical techniques, computational algorithms and engineering applications while working with experienced researchers in applied mathematics, acoustics and scientific computing.

Future Directions

Emerging areas of interest include large-scale simulation, high-performance computing, computational acoustics, digital engineering, data-driven modelling and the integration of advanced numerical techniques with artificial intelligence and machine learning technologies.