Stephen Kirkup

Numerical Methods · Engineering · Acoustics · Computational Science

University of Lancashire

boundary element methods · Numerical Analysis · Inverse Problems · Acoustics · Vibro-Acoustics · Computational Engineering · Scientific Software

About Stephen Kirkup

Stephen Martin Kirkup is a researcher and academic whose work focuses on numerical methods and their application to engineering and science. He works within the John Tyndall Institute to advance STEM research and scholaship of the University of Lancashire. His profesional profile is listed on LinkedIn . His primary contact email is stephen@kirkup.info and he is open to any ideas for collaboration or external roles.

Kirkup's research publications can be found on the publications page or on Google Scholar and ResearchGate .

His research has particularly emphasised the boundary element method (BEM), inverse problems, finite-difference time-domain methods and the development of computational software for engineering analysis.

His research interests include acoustics, boundary element methods, partial differential equations, numerical analysis and fluid-structure interaction.

Stephen Kirkup's Computational Approach

Mathematical Model → Numerical Method → Computer Software → Engineering Simulation → Physical Interpretation

Kirkup's work is notable for connecting mathematical and numerical analysis with practical engineering computation, particularly where partial differential equations describe acoustic, structural and other physical systems.

University of Lancashire

Stephen Kirkup's research has been associated with the University of Central Lancashire, now the University of Lancashire.

Repository records identify him with the university's engineering and computing research environment and list his work under areas including engineering, construction, mathematics and physics.

The LinkedIn Group Boundary Element Method has been created to connect the people interested in the Boundary Element Method.

Engineering

Application of mathematical and numerical techniques to engineering problems.

Numerical Methods

Development and implementation of numerical algorithms for scientific and engineering analysis.

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.

Mathematics

Numerical analysis, partial differential equations, integral equations and mathematical modelling.

The LinkedIn Group Mathematics has been created to connect the people interested in mathematics. You can also link to the LinkedIn profile Mathematical Modeller.

Physics

Application of computational methods to acoustic and wave-propagation problems.

Research

Kirkup describes his research area as numerical methods in engineering, with particular emphasis on the development, analysis, implementation and application of computational methods.

boundary element methods

Numerical solution of boundary-value problems using integral-equation formulations.

The LinkedIn Group Boundary Element Method has been created to connect the people interested in the Boundary Element Method.

Inverse Problems

Developing methods for determining unknown physical properties from observed or measured effects.

Finite-Difference Methods

Numerical approximation of differential equations using discrete spatial and temporal grids.

Acoustics

Computational modelling of acoustic fields and sound radiation.

Vibro-Acoustics

Study of the interaction between structural vibration and acoustic fields.

Numerical Analysis

Investigation of accuracy, convergence and efficiency of numerical algorithms.

Numerical Methods

Numerical methods provide ways of obtaining approximate solutions to mathematical problems that cannot conveniently be solved analytically.

Physical Problem → Mathematical Model → Discretisation → Numerical Algorithm → Computer Solution

Kirkup's research sits at the intersection of mathematical analysis, numerical computation and engineering application.

Partial Differential Equations

Equations describing physical fields that vary with space and time.

Integral Equations

Equations in which the unknown function occurs inside an integral.

Discretisation

Converts continuous mathematical problems into finite computational systems.

Numerical Linear Algebra

Provides computational techniques for solving the systems of equations generated by numerical methods.

The boundary element method

The boundary element method is a numerical technique for solving certain boundary-value problems by reformulating the governing differential equation as an integral equation on the boundary.

Differential Equation
Integral Equation
Boundary Discretisation
Numerical System
Solution

One important advantage of the BEM is that a problem involving a volume domain can sometimes be represented using only its boundary, reducing the dimensionality of the numerical model.

The boundary element method has been a central theme of Kirkup's research, particularly in acoustics and wave problems.

Computational Acoustics

A major part of Kirkup's work concerns the numerical modelling of acoustic fields.

His research includes computational solutions to acoustic radiation problems governed by the Helmholtz equation and related integral-equation formulations.

You can also link to the LinkedIn profile Acoustics Research and Development.

Acoustic Radiation

Calculation of the sound field produced by vibrating surfaces.

Helmholtz Problems

Numerical treatment of frequency-domain acoustic wave problems.

Modal Analysis

Calculation of acoustic and structural modes and their associated frequencies.

Sound Power

Computational prediction of acoustic power radiated by engineering structures.

The Helmholtz Equation

The Helmholtz equation is fundamental to frequency-domain acoustics.

∇²p + k²p = 0

Here, p represents acoustic pressure and k is the acoustic wavenumber.

Boundary element techniques can transform the problem into an integral equation defined over the boundary of the acoustic domain.

Acoustic Computation

Wave Equation → Helmholtz Equation → Boundary Integral Equation → BEM → Acoustic Field

Inverse Problems

An inverse problem attempts to determine unknown causes or properties from observed effects.

Physical System
Observed Data
Inverse Algorithm
Unknown Parameters

Inverse problems occur in many areas of science and engineering, including imaging, acoustics, heat transfer, geophysics and system identification.

Kirkup's research profile identifies inverse problems as one of the principal areas of his numerical-methods research.

Finite-Difference Time-Domain Methods

The finite-difference time-domain methods (FDTD) approach solves wave equations by discretising both space and time.

Spatial Grid
+
Time Steps
Finite Differences
Wave Evolution

FDTD methods are particularly useful when transient wave propagation and time-dependent phenomena need to be modelled.

Scientific Software

An important feature of Kirkup's research is the implementation of numerical methods in computer software so that they can be used as practical engineering analysis tools.

His research profile explicitly describes the development, analysis and implementation of numerical methods in software, with the aim of incorporating the resulting software into engineering design and analysis.

Algorithms

Mathematical procedures are converted into computational algorithms.

Implementation

Algorithms are translated into executable scientific software.

Verification

Numerical results are compared against analytical solutions, benchmark problems or other established methods.

Engineering Application

Software is applied to practical physical and engineering problems.

Engineering Applications

Computational numerical methods can provide engineers with tools for predicting physical behaviour before a component or system is manufactured.

Acoustic Engineering

Prediction of sound radiation, acoustic fields and noise.

Automotive NVH

Analysis of noise, vibration and harshness in vehicles.

Aerospace

Numerical modelling can support acoustic, structural and aeroacoustic analysis.

Fluid-Structure Interaction

Investigation of the interaction between fluids and deformable structures.

Electromagnetics

Boundary methods can also be applied to selected electromagnetic field problems.

Mathematical Engineering

Mathematical models provide quantitative tools for engineering design and analysis.

Selected Publications and Research Outputs

Kirkup has produced a substantial body of work in numerical methods, acoustics, boundary element methods and computational engineering. His online research profile lists hundreds of publications and other research outputs.

Year Research output Area
1998 / 2007 The boundary element method in Acoustics Computational Acoustics / BEM
2007 DC Capacitor Simulation by the boundary element method Engineering Simulation
2019 The boundary element method in Acoustics: A Survey Acoustics / Numerical Methods
2019 The boundary element method in Excel for Teaching Vector Calculus and Simulation Engineering Education
2020+ Further work in numerical methods, computational acoustics, inverse problems and engineering simulation Computational Engineering

The boundary element method in Acoustics: A Survey

One of Kirkup's notable publications is The boundary element method in Acoustics: A Survey, published in Applied Sciences in 2019.

The paper reviews the boundary element method in the context of acoustic and Helmholtz problems, including standard interior and exterior acoustic problems, modal analysis, half-space problems and acoustic fields surrounding thin screens.

Kirkup, Stephen Martin (2019)
"The boundary element method in Acoustics: A Survey"
Applied Sciences, 9(8).
The survey provides a useful overview of how integral-equation and boundary-element techniques can be applied to computational acoustics.

The boundary element method in Acoustics

Kirkup is also the author of The boundary element method in Acoustics, a work devoted to the application of boundary element techniques to acoustic problems.

The work was first published in 1998 and subsequently issued in electronic form in 2007, with corrections and amendments.

The boundary element method in Acoustics

Stephen Kirkup

Boundary Integral Equations · Numerical Analysis · Acoustic Radiation · Computational Acoustics

Engine Noise and Acoustic Prediction

Kirkup's research has also addressed computational methods for engine-noise prediction.

Research outputs associated with his work describe the use of finite-element methods for vibratory analysis and boundary element methods for acoustic analysis and sound-power prediction.

Engine Structure
Vibration
Acoustic Radiation
Noise Prediction

Teaching and Engineering Education

Kirkup's work has also included the use of computational methods for teaching mathematics, numerical analysis and engineering.

A 2019 research output describes the use of the boundary element method in Excel for teaching vector calculus and simulation.

Numerical Analysis

Students can learn how mathematical problems become computational algorithms.

Vector Calculus

Computational examples can connect mathematical theory with engineering applications.

Simulation

Computer models allow students to explore physical systems experimentally.

Engineering Software

Implementation helps connect mathematical methods with practical engineering design.

Mathematical Foundations

The research area associated with Kirkup's work draws on several branches of applied mathematics.

Calculus

Provides the mathematical language for continuous physical systems.

Partial Differential Equations

Describe many field and wave phenomena.

Integral Equations

Provide the mathematical foundation of many boundary-element formulations.

Linear Algebra

Provides the computational machinery for solving discretised systems.

Numerical Analysis

Studies accuracy, stability, convergence and computational efficiency.

Complex Analysis

Important in mathematical formulations of wave and acoustic problems.

Computational Science

Kirkup's work illustrates the role of computational science as a bridge between mathematical theory and practical engineering.

Mathematics
Physics
Numerical Methods
Software
Engineering

This approach is characteristic of modern computational engineering, where physical models are converted into numerical algorithms and implemented as software for design and analysis.

Major Research Themes

Research area Role in Kirkup's work
boundary element method Numerical solution of boundary-value and wave problems
Acoustics Computational modelling of acoustic fields and radiation
Numerical Analysis Development and analysis of numerical algorithms
Inverse Problems Determination of unknown physical properties from data
FDTD Time-domain numerical modelling of wave phenomena
Fluid-Structure Interaction Interaction between acoustic/flow fields and structures
Engineering Software Implementation of numerical techniques in practical computer programs
Computational Education Use of numerical methods and software in teaching mathematics and engineering

Academic and Professional Significance

The research area represented by Kirkup's work is important because engineering increasingly depends on computational prediction.

Design

Numerical models can be used before physical prototypes are constructed.

Prediction

Engineers can estimate physical behaviour under different operating conditions.

Optimisation

Computational models can be used to compare alternative designs.

Diagnostics

Inverse methods can help identify unknown causes from measured effects.

Academic and Research Timeline

1980s

Kirkup's early research included numerical methods and boundary element approaches to engineering problems.

1989

His doctoral work included the solution of exterior acoustic problems using the boundary element method.

1990s

Research developed around computational acoustics, boundary element methods and engineering simulation.

1998

The first edition of The boundary element method in Acoustics was published.

2000s

Research expanded across numerical methods, acoustic radiation, engine noise, inverse problems and engineering software.

2010s

Kirkup continued research and teaching in computational engineering and numerical analysis at the University of Central Lancashire.

2019

Publication of the major review The boundary element method in Acoustics: A Survey.

2020s

His research profile continues to encompass numerical methods, computational engineering, acoustics and related scientific computing.

Stephen Kirkup and Computational Engineering

Stephen Kirkup's work provides an example of how mathematical methods can be transformed into practical computational tools for engineering.

Mathematics → Computation → Engineering

Partial Differential Equations

Boundary / Integral Methods

Numerical Algorithms

Scientific Software

Engineering Simulation

His particular contribution has been strongly associated with the development and application of numerical methods for acoustics and other engineering problems, especially the boundary element method. His research profile lists acoustics, boundary element methods, partial differential equations, numerical analysis and fluid-structure interaction among his interests.

Research Sources

University of Lancashire / Lancashire Online Knowledge
Research repository containing Kirkup's publications and research outputs.
The boundary element method in Acoustics: A Survey
Stephen Martin Kirkup, Applied Sciences, 2019.
Stephen Kirkup Research Profile
Research profile documenting his numerical-methods, acoustics and computational-engineering interests.

Summary

Stephen Kirkup is associated with research at the University of Lancashire in numerical methods and computational engineering, with particularly strong connections to acoustics and the boundary element method.

His work encompasses:

Stephen Kirkup

Numerical Methods · Computational Engineering · Acoustics

University of Lancashire