Numerical analysis reports
The Numerical Analysis group published a series of reports detailed below. Some of these reports are available online. This series has now been subsumed into the Preprint series and the Mathematics Report series:
2007
1/2007 Weak constraints in four-dimensional variational (PDF-985Kb)
L.R. Watkinson, A.S. Lawless, N.K. Nichols and I. Roulstone
2/2007 Towards data assimilation for high resolution nested models (PDF-133Kb)
G.M. Baxter, S.L. Dance, A.S. Lawless, N.K. Nichols and S.P. Ballard
3/2007 Correlated observation errors in data assimilation (PDF-606KB)
L.M. Stewart, S.L. Dance and N.K. Nichols
4/2007 Modelling of forecast errors in geophysical fluid flows (PDF-181KB )
R.N. Bannister, D. Katz, M.J.P. Cullen, A.S. Lawless and N.K. Nichols
5/2007 Approximate Gauss-Newton methods using reduced order models(PDF-180KB)
A.S. Lawless, N.K. Nichols, C. Boess, A. Bunse-Gerstner
6/2007 Existence and properties of solutions for neural field equations (PDF-276KB)
P. beim Graben and R. Potthast
7/2007 Modelling the diurnal variability of sea surface temperatures (PDF-1.6MB)
S. Pimentel, K. Haines, N.K.Nichols
8/2007 The assimilation of satellite derived sea surface temperatures into a diurnal cycle model (PDF-648KB)
S. Pimentel, K. Haines, N.K.Nichols
9/2007 Orthogonality sampling for object visualization (PDF-829MB)
R. Potthast
10/2007 Simple models of changing bathymetry with data assimilation(PDF-338KB)
P.J. Smith, M.J. Baines, S.L. Dance, N.K. Nichols and T.R. Scott
2006
1/2006 Use of potential vorticity for incremental data assimilation
M.A. Wlasak, N.K. Nichols & I. Roulstone
2/2006 Using constraint preconditioners with regularized saddle-point problems
H.S. Dollar, N.I.M. Gould, W.H.A. Schilders & A.J. Wathen
3/2006 Constraint-style preconditioners for reqularized saddle point problems
H.S. Dollar
4/2006 Information content of spatially correlated observation errors
L.M. Stewart, S.L. Dance & N.K. Nichols
5/2006 A note on permutations for quadratic programming problems
H.S. Dollar
6/2006 Unbiased ensemble square root filters
D.M. Livings, S.L. Dance, and N.K. Nichols
7/2006 A Galerkin boundary element method for high frequency scattering by convex polygons
S.N.Chandler-Wilde and S. Langdon
8/2006 A comparison of potential vorticity-based and vorticity-based control variables
D. Katz, A.S. Lawless, N.K. Nichols1, M.J.P. Cullen and R.N. Bannister
9/2006 Small- and waiting-time behaviour of the thin-film equation
J.F. Blowey, J.R. King and S.Langdon
10/2006 Using model reduction methods within incremental 4D-Var
A.S.Lawless, N.K.Nichols, C.Boess and A. Bunse-Gerstner
11/2006 Scale analysis of observational information in data assimilation
G.M. Baxter, S.L. Dance, A.S. Lawless and N.K. Nichols
12/2006 Convergence and numerics of a multi-section method for scattering by three-dimensional rough surfaces
Eric Heinemeyer, Marko Lindner and Roland Potthast
13/2006 On source analysis by wave splitting with applications in inverse scattering of multiple obstacles
Fahmi Ben Hassen, Jijun Liu and Roland Potthast
2005
1/2005 A cell by cell adaptive mesh Lagrangian scheme for the numerical solution of the Euler Equations
J. M. Morrell
2/2005 Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements.
J. Schoeberl, J.M. Melenk, C. Pechstein, and S. Zaglmayr
3/2005 Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison.
T. Eibner, J.M. Melenk
4/2005 A singular vector perspective of 4D-Var: The spatial structure and evolution of baroclinic weather systems
C. Johnson, B. J. Hoskins, N. K. Nichols and S. P. Ballard
5/2005 Inner loop stopping criteria for incremental four-dimensional variational data assimilation
A.S. Lawless and N.K. Nichols
6/2005 Efficient evaluation of highly oscillatory acoustic scattering surface integrals
M. Ganesh, S. Langdon, I.H. Sloan
7/2005 A collocation method for high frequency scattering by convex polygons
S. Arden, S.N. Chandler-Wilde, S. Langdon
2004
1/2004 A singular vector perspective of 4D-VAR: Filtering and interpolating..
C. Johnson, N.K. Nichols and B.J. Hoskins
2/2004 An investigation of incremental 4D-Var using non-tangent linear models
A.S. Lawless, S.Gratton and N.K. Nichols
3/2004 Approximate iterative methods for variational data assimilation
A.S. Lawless, S. Gratton and N.K. Nichols
4/2004 Variational data assimilation for Hamiltonian problems
L.R. Stanton, A.S. Lawless, N.K. Nichols and I. Roulstone
5/2004 Very large inverse problems in atmosphere and ocean modelling
C. Johnson, N.K. Nichols and B.J. Hoskins
6/2004 Preconditioners for inhomogenous anisotropic problems in spherical geometry
D.E.Brown, N.K.Nichols and M.J.Bell
7/2004 A ghost fluid, moving finite volume plus remap method for compressible Euler flows
D.A. Bailey, P.K. Sweby and P. Glaister
8/2004 Generation of Arbitrary Lagragian-Eulerian (ALE) Velocities, based on monitor functions, for the solution of compressible flow equations
B.V. Wells, M.J. Baines and P. Glaister
9/2004 Approximate Gauss-Newton methods for nonlinear least squares problems
S.Gratton, A.S. Lawless and N.K. Nichols
10/2004 A local error analysis of the boundary concentrated FEM
T. Eibner and J.M. Melenk
11/2004 On Approximation in Meshless Methods
J.M. Melenk
12/2004 On Approximation in Meshless Methods
T. Eibner and J.M. Melenk
2003
1/2003 Lagrange-Remap methods for the Euler Equations for single and multi gas flow..
D.A. Bailey
2002
1/2002 Four Dimensional Variational Data Assimilation in the Presence of Idealised Rapidly Growing Weather Systems
C Johnson, N.K. Nichols, B.J. Hoskins, S.P. Ballard & A.S. Lawless
2/2002 A moving mesh method for non-linear parabolic problems
K.W. Blake & M.J. Baines
3/2002 Linearising the Kepler Problem for 4D-Var Data Assimilation.
Laura Stanton
4/2002 Crowded Macroscopic and Microscopic Models for Pedestrian Dynamics
Penny Marno
5/2002 On the numerical solution of selected integrable nonlinear wave equations
Malachy McConnell
2001
1/2001 Numerical Solution of Hyperbolic Systems of conservation Laws with Source Terms - Part I.
A C Lemos, M J Baines and N K Nichols
2/2001 Numerical Modelling of Traffic on the M25 Motorway: Part I.
Joanne Morgan
3/2001 Numerical Modelling of Traffic on the M25 Motorway: Part II
Joanne Morgan
4/2001 A comparison of two methods for developing a linearisation of the shallow water model
A S Lawless, N.K.Nichols and S. P Ballard
2000
1/2000 Mesh Movement by Mass Conservation.
K.W. Blake
2/2000 Numerical Formulations for approximating the Equations Governing Bed-Load Sediment Transport in Channels and Rivers.
J. Hudson and P.K. Sweby
3/2000 A New Method for Solving the 2-D Advection Equation.
A. Laird
4/2000 Finite Differences Applied to Stochastic Problems in Pricing Derivatives.
S. Christodoulou
5/2000 Galerkin Methods for Coupled Integral Equations.
S.H. Man
6/2000 A Marker and Cell Solution of the Incompressible Navier-Stokes Equations for Free Surface Flow.
B. Weston
7/2000 The Solution of Steady PDEs on Adjustable Meshes in Multidimensions Using Local Descent Methods.
M.J. Baines
8/2000 Multidimensional Least Squares Fluctuation Distribution Schemes with Adaptive Mesh Movement for Steady Hyperbolic Equations.
M.J. Baines, S.J. Leary and M.E. Hubbard
1999
1/99 On the accuracy of one-dimensional models of steady converging/diverging open channel flows.
M.E. Hubbard
2/99 Numerical techniques for the Shallow Water Equations.
J. Hudson
3/99 Flux difference splitting and the balancing of source terms and flux gradients.
M.E. Hubbard and P.Garcia-Navarro
4/99 Aspects of multidimensional upwinding: time-dependent nonlinear systems, source terms, spherical geometries and three-dimensional grid adaptation.
M.E. Hubbard
5/99 High Order Advection Schemes: Automatic Generation.
R. Lashley
6/99 Robust Eigenstructure Assignment in Quadratic Matrix Polynomials : Nonsingular Case.
N.K. Nichols & J Kautsky
7/99 Godunov Methods.
P.K. Sweby
8/99 The Use of Moving Grids in Contour Zoning.
K.W. Blake
9/99 Adjoint Methods in Data Assimilation for Estimating Model Error.
A.K. Griffiths and N.K. Nichols
10/99 High Order Advection Schemes; Automatic Generation.
R.K. Lashley
11/99 Moving Finite element, Least Squares and Finite Volume Approximations of Steady and Time-Dependent PDEs in Multidimensions.
M.J. Baines
1998
1/98 Multidimensional upwind fluctuation distribution schemes for scalar time dependent problems.
M.E. Hubbard and P.L. Roe
2/98 Multidimensional slope limiters for MUSCL-type finite volume schemes..
M.E. Hubbard
3/98 Bifurcation analysis of eigenstructure assignment control in a simple nonlinear aircraft model.
L.P. Gibson, N.K. Nichols and D.M. Littleboy
4/98 Application of variational data assimilation to the Lorenz equations using the adjoint method.
M.A. Wlasek and N.K. Nichols
5/98 Adjoint methods for treating model error in data assimilation.
A.K. Griffith and N.K. Nichols
6/98 Fluctuation distribution schemes on adjustable meshes for scalar hyperbolic equations.
M.J. Baines and S.J. Leary
7/98 Interim report on the application of non-linear optimal control techniques in open channel water management.
I. Villanueva
8/98 Multidimensional slope limiters for MUSCL-type finite volume schemes II - on improving existing unstructured grid techniques.
M.E. Hubbard
1997
1/97 Conservative multidimensional upwinding for the steady two-dimensional shallow water equations.
M.E. Hubbard and M.J. Baines
2/97 On variational and least squares methods with adjustable nodes.
M.J. Baines
3/97 Least squares, equidistribution and conservation.
M.J. Baines
4/97 Interface tracking using Eulerian methods with a Lagrangian phase.
P. Sims
5/97 Modal coupling in linear control systems using robust eigenstructure assignment.
D.M. Littleboy and N.K. Nichols
6/97 Least squares minimisation and a steepest descent method for the scalar advection equation and a Cauchy-Riemann system on an adaptive grid.
M.E. Hubbard
7/97 A collection of MATLAB subroutines for the implementation of damped algebraic Riccati equations.
J.J. Hench
8/97 A note on duality in a scalar hyperbolic equation.
M.J. Baines
9/97 Numerical experiments on the solution of a scalar advection equation by least squares on optimal grids.
S.J. Leary
10/97 Variational data assimilation: a study.
M.A. Wlasek
11/97 An upwind scheme for the 2-d shallow water equations with applications.
P. Brufau
1996
1/96 Evaluation of the proposed new unified model scheme vs the current unified model scheme on the shallow water equations.
A.J. Malcolm
2/96 Accounting for model error in data assimilation using adjoint methods.
A.K.Griffith and N.K.Nichols
3/96 Optimal strategies for the control of wave energy converters with various power-take-off mechanisms.
N.K. Nichols and A. Crossley
4/96 Numerical variational techniques on adjustable meshes.
M.J. Baines
5/96 A note on damped algebraic Riccati equations.
C-Y. He, J.J. Hench and V. Mehrmann
6/96 A first principles derivation of a simple non-linear aerodynamic model.
J.J. Hench and N.K. Nichols
7/96 Approximate solutions of partial differential equations on optimal meshes using variational principles.
M.J. Baines
1995
1/95 Computation of the net present value of a reservoir with uncertain data..
M.P. Dainton and N.K. Nichols
2/95 Comparisons of some steady state Saint-Venant solvers for some test problems with analytic solutions.
I. MacDonald, M.J. Baines, N.K.Nichols and P.G. Samuels
3/95 Steady open channel test problems with analytic solutions.
I. MacDonald, M.J. Baines, N.K. Nichols and P.G. Samuels
4/95 Conservative multidimensional upwinding for the shallow water equations.
M.E. Hubbard, P. Garcia-Navarro and M.J. Baines
5/95 A dynamical approach study of some explicit and implicit TVD schemes and their convergence to steady-state solutions.
P.A. Burton and P.K. Sweby
6/95 Use of a discrete norm in best piecewise constant approximation of continuous functions on irregular grids.
M.J. Baines
7/95 An MFE-like method for best approximation.
M.J. Baines
8/95 Properties of a grid movement algorithm.
M.J. Baines
9/95 Grid adaptation for 1-D unsteady problems.
P. Garcia-Navarro
10/95 Direct computation of stochastic flow in reservoirs with uncertain parameters.
M.P. Dainton, M.H. Goldwater, N.K. Nichols
11/95 Improving second moment conservation in semi-Lagrangian methods.
A. Priestley and P. Garcia-Navarro
12/95 Comparison of explicit and implicit TVD schemes for the shallow water equations on a sphere.
A.J. Crossley
13/95 The use of variational principles in determining approximations to continuous and discontinuous shallow water flows.
S.L. Wakelin, M.J. Baines and D. Porter
1994
1/94 The state estimation of flow demands in gas networks from sparse pressure telemetry.
N.K. Nichols and S.M. Stringer
2/94 A numerical method for the computation of the analytic singular value decomposition.
S.J.G. Bell and N.K. Nichols
3/94 Genuinely multidimensional upwinding for the 2D shallow water equations.
P. Garcia-Navarro, M.E. Hubbard and A. Priestley
5/94 Gaussian elimination with pivoting for multi-diagonal systems.
C.I. Christov
6/94 Test problems with analytic solutions for steady open channel flow.
I. MacDonald
7/94 Analysis and computation of steady open channel flow using a singular perturbation.
I. MacDonald, M.J. Baines and N.K. Nichols
8/94 Grid adaptation and multidimensional upwinding.
M.E. Hubbard
9/94 Direct solution of reservoir flow equations with uncertain parameters.
M.P. Dainton, M. Goldwater, N.K. Nichols
10/94 Data assimilation using optimal control theory..
A.K. Griffith and N.K. Nichols
11/94 Data assimilation using observers.
A.K. Griffith and N.K. Nichols
1993
1/93 On algorithms for best L2 fits to continuous functions with variable nodes.
M.J. Baines
2/93 A hybrid central/upwind approach to the solution of the one dimensional Euler equations.
M.E. Hubbard
3/93 Error measurements for semi-Lagrangian schemes.
C.J. Smith
4/93 The Lagrange-Galerkin method: quadrature is dead, long live inexact integration.
A. Priestley
5/93 Application of the Taylor-Galerkin method to transport problems in subsurface hydrology.
K.J. Neylon
6/93 A conservative and shape-preserving semi-Lagrangian method for the solution of the shallow water equations.
P. Garcia-Navarro and A. Priestley
7/93 A survey of genuinely multi-dimensional upwinding techniques.
M.E. Hubbard
8/93 Numerical experiences with Bi-CGSTAB on an advection-diffusion..
K.J. Neylon
9/93 Numerical methods for the solution of systems of uncertain steady-state differential equations.
M.P. Dainton
10/93 The application of an implicit TVD method for water flow modelling in channels and pipes.
P. Garcia-Navarro and A. Priestley
11/93 Integral operators of Sturm-Liouville type.
D. Porter and D.S.G. Stirling
13/93 Dynamic-algebraic equations and control system design.
N.K. Nichols
1992
1/92 ALGORITHM: Andy's Lagrange Galerkin Offers Really Immense Time steps and Higher order monotonicity. The multidimensional monotone and nearly conservative Lagrange-Galerkin method with conforming elements.
A. Priestley
2/92 A quasi-conservative version of the semi-Lagrangian advection scheme.
A. Priestley
3/92 The implementation of a direct domain decomposition method on a small transputer system.
K.J. Neylon
4/92 Variational principles for free surface flows.
S.L. Wakelin
5/92 MASTERFUL - Monotonic Adaptive Solutions of Transient Equations using Recovery, Fitting, Upwinding and Limiters.
M.J. Baines
6/92 The rate of convergence of the viscosity method for nonlinear hyperbolic systems.
Y.G. Lu, P.K. Sweby and K. Chen
7/92 Backwater analysis for channel flows and side-weirs using ides.
A. Priestley
8/92 The application of Roe's scheme to two problems of engineering interest.
A. Priestley
9/92 Steady flow in channels with decreasing discharge: theory and computation.
D. Porter and A. Priestley
10/92 Approximations to channel flows using variational principles..
S.L. Wakelin
11/92 An analysis of some higher-order triangular elements and their susceptibility to hourglassing in Lagrangian fluid simulations.
A. Priestley
12/92 Optimal growth strategies when mortality and production rates are size-dependent.
N. Perrin, R.M. Sibly and N.K. Nichols
1991
1/91 The Taylor Galerkin method for advection on the sphere.
A. Priestley
2/91 On the relationship between the moving finite element procedure and best piecewise linear L2 fits with adjustable nodes.
M.J. Baines
3/91 Regularization of descriptor systems by derivative and proportional state feedback.
N.K. Nichols, A Bunse-Gerstner and V. Mehrmann
4/91 Equidistribution and the Legendre transformation.
M.J. Baines and S.L Wakelin
5/91 An investigation of the form of an optimal controller in a tidal power generation scheme with two controls.
Z.G. Xu and N.K. Nichols
6/91 Hydrodynamic modelling and optimal control of tidal power schemes in long estuaries.
Z.G. Xu and N.K. Nichols
7/91 On spurious asymptotic numerical solutions of 2x2 systems of ODEs.
P.K. Sweby and H.C. Yee (NASA)
8/91 Numerical methods for optimal control problems with state constraints.
S. Lyle and N.K. Nichols
9/91 The Taylor-Galerkin method for the shallow water equations on the sphere.
A. Priestley
10/91 On time step selection for solving 1D nonlinear diffusion equations.
K.Chen, M.J. Baines and P.K. Sweby
11/91 An adaptive time stepping strategy for the ASWR semiconductor diffusion model simulator.
K.Chen, M.J. Baines and P.K. Sweby
12/91 The Legendre transformation and grid generation in two dimensions..
S.L. Wakelin
13/91 Black oil reservoir simulation in 1-D via the higher order Godunov method.
E.M. Dicks
14/91 On unconditionally linearly stable centred and upwind semi-implicit methods for convection and convection diffusion problems.
M.J. Baines
15/91 "PLAGIARISM" - The monotone and nearly conservative Lagrange-Galerkin method.
A. Priestley
16/91 Shock fitting for the 2-D Euler equations.
P.D. Arnold
1990
1/90 A survey of some data-dependent criteria for triangular tessellations using fixed nodes.
A. Malcolm
2/90 A comparison of the directional difference scheme and Roe's scheme for the approximate solution of transient flow of an ideal gas in a pipe.
S. Emmerson
3/90 On spurious steady-state solutions of explicit Runge-Kutta schemes.
P.K. Sweby, H.C. Hee (NASA) and D.F. Griffiths (Dundee)
4/90 On simplification of multiblock/multigrid interaction for cell-vertex finite volume approximation of compressible fluid flow.
M. Aves
5/90 A quasi-Riemann method for the solution of one-dimensional shallow water flow.
A. Priestley
6/90 On best piecewise linear L2 fits with adjustable nodes.
M.J. Baines and N. Carlson (Univ. of California)
7/90 Robust pole assignment for structured perturbations.
J. Kautsky and N.K. Nichols
8/90 The form of optimal controllers for tidal-power-generation schemes.
T.P. Andrews
9/90 Shock structure for physical gases.
P.C. Samuels
10/90 A search for new finite elements to be used in conjunction with free-Lagrangian methods.
A. Priestley
11/90 Moving finite element procedures and multivalued solutions.
M.J. Baines and C.P. Reeves
12/90 On best piecewise constant L2 fits with adjustable nodes.
M.J. Baines
13/90 Analysis and experiments of a set of three-level semi-implicit finite difference schemes for nonlinear parabolic equations.
K. Chen
14/90 Conjugate gradient methods for the solution of boundary integral equations on a piecewise smooth boundary.
K. Chen
15/90 On best piecewise linear L2 fits with adjustable nodes: the 2-D case.
M.J. Baines
16/90 Data-dependent criteria for nodal placement with fixed connectivity in triangular grids.
A. Malcolm
17/90 On stability radius of generalized state-space systems.
R. Byers and N.K. Nichols
18/90 Experiments with 2-D shock fitting for the Euler equations.
P.D. Arnold
1989
1/89 Shocked flow in nozzles.
J. Wixcey
2/89 The spectral Lagrange Galerkin method for the atmospheric transportation of pollutants.
A. Priestley
3/89 A practical model for heavy oil recovery.
R. Brown
4/89 The spectral Lagrange-Galerkin method for the atmospheric transportation of pollutants. Part II. non-exact integration.
A. Priestley
5/89 Moving finite elements and approximate Legendre transformations.
M.J. Baines
6/89 Source terms and conservation laws: a preliminary discussion.
P.K. Sweby
7/89 The application of optimal control theory to tidal power generation problems.
R. Moody
8/89 The numerical solution of one-dimensional shallow-water problems using the Taylor-Galerkin method.
R. Moody
9/89 The spectral Lagrange-Galerkin method for atmosphere transportation of pollutants. Part III. The atmosphere transportation of pollutants.
A. Priestley
10/89 Foundations for the study of systems of conservation laws with and without diffusion.
P. Samuels
11/89 On derivative and proportional feedback design for descriptor systems.
A. Bunse-Gerstner, Volker Mehrmann, N.K. Nichols.
12/89 Shock behaviour and diffusion.
P. Samuels
13/89 Roe-type schemes for super-critical flows in rivers.
A. Priestley
14/89 On stability of descriptor systems.
R. Byers, and N.K. Nichols
15/89 On the convergence of the Ritz-Galerkin technique for solving two-dimensional optimal shape problems.
S. Lyle and N.K. Nichols
16/89 Inequality constrained finite elements and conjugate gradients.
N.R.C. Birkett
17/89 A comparison between two moving finite element methods.
C.P. Reeves
1988
4/88 Weak, non-symmetric shocks in one-dimension.
P. Samuels
5/88 Comments on the numerical integration of a class of singular perturbation problems.
N.K. Nichols
6/88 Interfacing of an oxidation model with the two-dimensional moving finite element of dopant diffusion.
N.S. Cooper
7/88 An analysis of properties of the shock tip in two dimensional steady flow using conservation equations.
P. Samuels
8/88 Optimisation of steam injection into an oil reservoir.
R. Brown
9/88 Roe's scheme, Euler equations, Cartesian grids, non-Cartesian geometries, rigid walls and there's more.
A. Priestley
10/88 Stability of descriptor systems.
R. Byers (Univ of Kansas) and N.K. Nichols
11/88 On the solution of nonlinear diffusion equations.
M.J. Baines
12/88 Compressible flow in ducts - Analytic aspects.
J. Wixcey
13/88 Compressible flow in ducts - Variational aspects.
J. Wixcey
14/88 Compressible flow in ducts - Adaptive grids.
J. Wixcey
15/88 Numerical approximation of the Legendre transformation.
M.J. Baines
16/88 Roe's scheme, Euler equations, Cartesian grids, non-Cartesian geometries, rigid walls - The continuing story.
A. Priestley
17/88 Output feedback via state feedback and least squares.
S. Slade
18/88 The implementation of boundary conditions in the application of Roe's scheme to aeronautical flows on Cartesian grids.
A. Priestley