Lawrence Mulholland

Staff Engineer / Technical Lead

Lawrence has over 30 years' experience supporting, writing and managing a range of numerical codes for CPU and other computing platforms. He is Technical Lead of Numerical Analysis within the Numerical Software Team and is jointly responsible, with other technical leads for algorithmic content of NAG Library products. Has also been responsible for the development and release of the NAG AD Library. His research and work areas include:

  • Linear Algebra 
  • Sparse Eigenproblems 
  • FFTs 
  • Differential Equations 
  • Algorithmic Differentiation (AD) 

    Specific Technical Experience

    Numerical code for processor vendors
    Lawrence has managed projects to produce and maintain complete numerical libraries for global CPU vendors.
    Design and development of a Numerical AD Library
    Lawrence managed, designed and is the principal developer for the NAG AD Library. 
    Design and development of parallel routines
    Lawrence worked with others at NAG, and our collaborators to devise, design and develop new algorithmic approaches that are most appropriate for current multi core and many core processor architectures.
    Development of many ODE, FFT, Linear Algebra and RNG codes
    Lawrence has developed numerical routines in many important areas for specific client requirements and for the NAG Library project. He also produces clear technical directions and descriptions of appropriate usage and limitations for a range of numerical solutions.
    Problem formulation advice
    Lawrence has been an advisor on alternative ways of presenting and solving real world numerical problems for many clients in a wide range of subject areas including astrophysics, finance, retail data, energy and climate science.
    Training delivery
    Lawrence has developed and presented training courses on writing numerical code as well as course and seminars on the use of specific typed of routines and methods. He has delivered these courses for a range of different technical audiences in finance and other fields.

    Mathematical Expertise

    • Linear Algebra
    • FFTs
    • Sparse eigenproblems
    • Nonlinear systems
    • PDEs and ODEs
    • Fitting and Interpolation

    Computing Expertise

    • Fortran
    • C
    • OpenMP


    • Ph.D, Pseudospectral methods for PDEs, Strathclyde University
    • Postdoc on Sound Wave propagation through tube bundles, Keele University
    • Postdoc on adaptivity in psuedospectral solution of near-singular evolutionary problems, Strathclyde University
    • BSc, Mathematics (Numerical Analysis), Strathclyde University

    Honours & Awards

    • BSc (Hons I), Strathclyde
    • TQ in Mathematics and computing; DipEd (Glasgow)

    Papers & Talks

    Pseudospectral Solution of Near-Singular Problems using Numerical Coordinate Transformations Based on Adaptivity
    L. S. Mulholland, W.-Z. HUANG, D. M. Sloan
    Journal: Siam Journal on Scientific Computing , Vol. 19, No. 4, 1998

    Solution of Evolutionary Partial Differential Equations Using Adaptive Finite Differences with Pseudospectral Post-processing
    L.S. Mulholland, Y.Qui and D.M.Sloan
    Journal of Computational Physics, Vol. 131, 1997

    Multi-Directional Sound Wave Propagation Through a Tube Bundle
    L.S. Mulholland, Maria Heckl
    Journal: Journal of Sound and Vibration, Vol. 176, No. 3, 1994

    Some Recent Developments in the Theory of Acoustic Transmission in Tube Bundles
    Maria A. Heckl, L.S. Mulholland
    Journal: Journal of Sound and Vibration, Vol 179, No. 1, 1995

    Sound propogation in a steam generator: experimental and theoretical results
    D. Firth, Maria A. Heckl, J.A. McKnight, L.S. Mulholland and R. Rowley
    Nuclear Energy, Vol. 32, No. 6, 1993

    An Implementation of the BLAS on the i860: A RISC Approach to Software for RISC Devices
    Bob Wilkinson, Lawrence S. Mulholland
    Conference: Conference on Algorithms and Hardware for Parallel Processing - CONPAR , pp. 283–294, 1992

    The role of preconditioning in the solution of evolutionary partial differtial equations by implicit Fourier pseudospectral methods
    L.S. Mulholland, D.M. Sloan
    Journal of Comptational and Applied Mathematics, Vol. 42, 1992

    The Effect of Filtering on the Psuedospectral Solution of Evolutionary Partial Differential Equations Special
    L.S. Mulholland, D.M. Sloan
    Journal: Journal of Computational Physics, Vol. 96, No. 2, 1991