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2020

Near critical, self-similar, blow-up solutions of the generalised Korteweg–de Vries equation: Asymptotics and computations

Amodio, P., Budd, C. J., Koch, O., Rottschäfer, V., Settanni, G. & Weinmüller, E., 1 Jan 2020, In : Physica D: Nonlinear Phenomena. 401, 132179.

Research output: Contribution to journalArticle

2019

Error estimates for semi-Lagrangian finite difference methods applied to Burgers' equation in one dimension

Cook, S., Budd, C., Hill, A. & Melvin, T., 1 Nov 2019, In : Applied Numerical Mathematics. 145, p. 261-282 22 p.

Research output: Contribution to journalArticle

Modelling the view factor of a ‘grain-like’ observer near a tilted pool fire via planar approximation approach

Budd, C. J. & Ugwu, U. O., 1 Jan 2019, In : Applied Mathematical Modelling. 65, p. 23-33 11 p.

Research output: Contribution to journalArticle

Open Access
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2 Citations (Scopus)
16 Downloads (Pure)

The moving mesh semi-Lagrangian MMSISL method

Budd, C., 15 Sep 2019, In : Journal of Computational Physics. 393, p. 484-502 19 p.

Research output: Contribution to journalArticle

Open Access
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1 Citation (Scopus)
8 Downloads (Pure)
2018

Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements

McRae, A. T. T., Cotter, C. J. & Budd, C. J., 24 Apr 2018, In : SIAM Journal on Scientific Computing. 40, 2, p. A1121-A1148

Research output: Contribution to journalArticle

Open Access
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5 Citations (Scopus)
47 Downloads (Pure)

The scaling and skewness of optimally transported meshes on the sphere

Budd, C. J., McRae, A. T. T. & Cotter, C. J., 15 Dec 2018, In : Journal of Computational Physics. 375, p. 540-564 25 p.

Research output: Contribution to journalArticle

Open Access
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1 Citation (Scopus)
18 Downloads (Pure)
2017
Open Access
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5 Citations (Scopus)
88 Downloads (Pure)
2016

Chevron folding patterns and heteroclinic orbits

Budd, C. J., Chakhchoukh, A. N., Dodwell, T. J. & Kuske, R., 1 Sep 2016, In : Physica D: Nonlinear Phenomena. 330, p. 32-46 15 p.

Research output: Contribution to journalArticle

Open Access
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1 Citation (Scopus)
31 Downloads (Pure)

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

Weller, H., Browne, P., Budd, C. & Cullen, M., 1 Mar 2016, In : Journal of Computational Physics. 308, p. 102-123 22 p.

Research output: Contribution to journalArticle

Open Access
11 Citations (Scopus)
52 Downloads (Pure)

Multilayer asymptotic solution for wetting fronts in porous media with exponential moisture diffusivity

Budd, C. J. & Stockie, J. M., May 2016, In : Studies in Applied Mathematics. 136, 4, p. 424-458

Research output: Contribution to journalArticle

Open Access
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88 Downloads (Pure)
2015

Global blow-up for a semilinear heat equation on a subspace

Budd, C. J., Dold, J. W. & Galaktionov, V. A., Oct 2015, In : Proceedings of the Royal Society of Edinburgh Section A - Mathematics. 145, 5, p. 893 - 923 31 p.

Research output: Contribution to journalArticle

Open Access
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4 Citations (Scopus)
111 Downloads (Pure)

The effect of numerical model error on data assimilation

Jenkins, S., Smith, N., Budd, C. & Freitag, M., 15 Dec 2015, In : Journal of Computational and Applied Mathematics. 290, p. 567-588

Research output: Contribution to journalArticle

Open Access
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2 Citations (Scopus)
119 Downloads (Pure)

The geometry of r-adaptive meshes generated using optimal transport methods

Budd, C., Walsh, E. & Russell, R., 1 Feb 2015, In : Journal of Computational Physics. 282, p. 113-137 25 p.

Research output: Contribution to journalArticle

Open Access
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9 Citations (Scopus)
129 Downloads (Pure)
2014

Asymptotical computations for a model of flow in saturated porous media

Amodio, P., Budd, C. J., Koch, O., Settanni, G. & Weinmüller, E., 15 Jun 2014, In : Applied Mathematics and Computation. 237, p. 155-167 13 p.

Research output: Contribution to journalArticle

Open Access
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7 Citations (Scopus)
123 Downloads (Pure)

Fast three dimensional r-adaptive mesh redistribution

Browne, P. A., Budd, C. J., Piccolo, C. & Cullen, M., 15 Oct 2014, In : Journal of Computational Physics. 275, p. 174-196 23 p.

Research output: Contribution to journalArticle

14 Citations (Scopus)
Open Access
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8 Citations (Scopus)
119 Downloads (Pure)
2013

Monge–Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem

Budd, C. J., Cullen, M. J. P. & Walsh, E. J., 1 Mar 2013, In : Journal of Computational Physics. 236, p. 247-270 34 p.

Research output: Contribution to journalArticle

25 Citations (Scopus)

Resolution of sharp fronts in the presence of model error in variational data assimilation

Freitag, M. A., Nichols, N. K. & Budd, C. J., Apr 2013, In : Quarterly Journal of the Royal Meteorological Society. 139, 672, p. 742-757 16 p.

Research output: Contribution to journalArticle

10 Citations (Scopus)

The origin of power-law emergent scaling in large binary networks

Almond, D. P., Budd, C. J., Freitag, M. A., Hunt, G. W., McCullen, N. J. & Smith, N. D., 15 Feb 2013, In : Physica A: Statistical Mechanics and its Applications. 392, 4, p. 1004-1027

Research output: Contribution to journalArticle

Open Access
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9 Citations (Scopus)
128 Downloads (Pure)
2012

A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints

Browne, P. A., Budd, C., Gould, N. I. M., Kim, H. A. & Scott, J. A., 21 Dec 2012, In : International Journal for Numerical Methods in Engineering. 92, 12, p. 1026-1043 18 p.

Research output: Contribution to journalArticle

15 Citations (Scopus)
7 Citations (Scopus)
208 Downloads (Pure)

Multi-layered folding with voids

Dodwell, T. J., Hunt, G. W., Peletier, M. A. & Budd, C. J., Apr 2012, In : Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences. 370, 1965, p. 1740-1758 19 p.

Research output: Contribution to journalArticle

16 Citations (Scopus)

Self-similar voiding solutions of a single layered model of folding rocks

Dodwell, T. J., Peletier, M. A., Budd, C. J. & Hunt, G. W., 2012, In : SIAM Journal on Applied Mathematics. 72, 1, p. 444-463 20 p.

Research output: Contribution to journalArticle

Open Access
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10 Citations (Scopus)
115 Downloads (Pure)
2011

A comparison of models and methods for simulating the microwave heating of moist foodstuffs

Budd, C. J. & Hill, A. D. C., 31 Jan 2011, In : International Journal of Heat and Mass Transfer. 54, 4, p. 807-817 11 p.

Research output: Contribution to journalArticle

18 Citations (Scopus)

Breathers in a pinned mechanical lattice

Green, S. C., Budd, C. J. & Hunt, G. W., 2011, In : SIAM Journal on Applied Dynamical Systems. 10, 1, p. 66-91 26 p.

Research output: Contribution to journalArticle

2 Citations (Scopus)
File
11 Citations (Scopus)
82 Downloads (Pure)

Introduction to special issue on reflections in nonlinear mechanics

Budd, C., Champneys, A., Lord, G. & Virgin, L., Feb 2011, In : IMA Journal of Applied Mathematics. 76, 1, p. 1 1 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)

Regularization techniques for ill-posed inverse problems in data assimilation

Budd, C., Freitag, M. A. & Nichols, N. K., Jul 2011, In : Computers and Fluids. 46, 1, p. 168-173 6 p.

Research output: Contribution to journalArticle

14 Citations (Scopus)

The dynamics of a simplified pinball machine

Pring, S. R. & Budd, C. J., Feb 2011, In : IMA Journal of Applied Mathematics. 76, 1, p. 67-84 18 p.

Research output: Contribution to journalArticle

8 Citations (Scopus)
2010

How to adaptively resolve evolutionary singularities in differential equations with symmetry

Budd, C. J. & Williams, J. F., Mar 2010, In : Journal of Engineering Mathematics. 66, 1-3, p. 217-236 20 p.

Research output: Contribution to journalArticle

16 Citations (Scopus)

Image-model coupling: application to an ionospheric storm

Smith, N. D., Pokhotelov, D., Mitchell, C. N. & Budd, C., 20 Aug 2010, In : Nonlinear Processes in Geophysics. 17, 4, p. 361-369

Research output: Contribution to journalArticle

1 Citation (Scopus)

L1-regularisation for ill-posed problems in variational data assimilation

Freitag, M. A., Nichols, N. K. & Budd, C. J., Dec 2010, In : PAMM - Proceedings in Applied Mathematics and Mechanics. 10, 1, p. 665 -668 4 p.

Research output: Contribution to journalArticle

The dynamics of regularized discontinuous maps with applications to impacting systems

Pring, S. R. & Budd, C. J., 19 Feb 2010, In : SIAM Journal on Applied Dynamical Systems. 9, 1, p. 188-219 32 p.

Research output: Contribution to journalArticle

2009

Adaptivity with moving grids

Budd, C. J., Huang, W. & Russell, R. D., May 2009, In : Acta Numerica. 18, p. 111-241 131 p.

Research output: Contribution to journalArticle

138 Citations (Scopus)

Image-model coupling: a simple information theoretic perspective for image sequences

Smith, N. D., Mitchell, C. N. & Budd, C. J., 20 Mar 2009, In : Nonlinear Processes in Geophysics. 16, 2, p. 197-210 14 p.

Research output: Contribution to journalArticle

Open Access
1 Citation (Scopus)

Moving mesh generation using the parabolic Monge–Ampère equation

Budd, C. J. & Williams, J. F., 2009, In : SIAM Journal on Scientific Computing. 31, 5, p. 3438-3465 28 p.

Research output: Contribution to journalArticle

42 Citations (Scopus)
2008

Bifurcations in Nonsmooth Dynamical Systems

di Bernardo, M., Budd, C. J., Champneys, A. R., Kowalczyk, P., Nordmark, A. B., Tost, G. O. & Piiroinen, P. T., 2008, In : Siam Review. 50, 4, p. 629-701 73 p.

Research output: Contribution to journalArticle

219 Citations (Scopus)
17 Citations (Scopus)
2007

An evaluative study on ESO and SIMP for optimising a cantilever tie-beam

Edwards, C. S., Kim, H. A. & Budd, C. J., 2007, In : Structural and Multidisciplinary Optimization. 34, 5, p. 403-414 12 p.

Research output: Contribution to journalArticle

31 Citations (Scopus)
15 Citations (Scopus)
2006

Computation of self-similar solution profiles for the nonlinear Schrodinger equation

Budd, C., Koch, O. & Weinmuller, E., 2006, In : Computing. 77, 4, p. 335-346 12 p.

Research output: Contribution to journalArticle

17 Citations (Scopus)

Corner bifurcations in non-smoothly forced impact oscillators

Budd, C. J. & Piiroinen, P. T., 2006, In : Physica D: Nonlinear Phenomena. 220, 2, p. 127-145 19 p.

Research output: Contribution to journalArticle

45 Citations (Scopus)

From nonlinear PDEs to singular ODEs

Budd, C., Koch, O. & Weinmuller, E., 2006, In : Applied Numerical Mathematics. 56 Mar-Apr, 3-4, p. 413-422 10 p.

Research output: Contribution to journalArticle

21 Citations (Scopus)

Parabolic Monge-Ampère methods for blow-up problems in several spatial dimensions

Budd, C. J. & Williams, J. F., 12 May 2006, In : Journal of Physics A: Mathematical and General. 39, 19, p. 5425-5444 20 p.

Research output: Contribution to journalArticle

33 Citations (Scopus)

Serial parallel folding with friction: a primitive model using cubic B-splines

Hunt, G. W., Edmunds, R., Budd, C. J. & Cosgrove, J. W., 2006, In : Journal of Structural Geology. 28, 3, p. 444-455 12 p.

Research output: Contribution to journalArticle

11 Citations (Scopus)
2005

Adaptive geometric integrators for Hamiltonian problems with approximate scale invariance

Blanes, S. & Budd, C. J., 2005, In : SIAM Journal on Scientific Computing. 26, 4, p. 1089-1113 25 p.

Research output: Contribution to journalArticle

11 Citations (Scopus)

Bifurcations of periodic solutions satisfying the zero-Hamiltonian constraint in reversible differential equations

Beardmore, R. E., Peletier, M. A., Budd, C. J. & Wadee, M. A., 2005, In : SIAM Journal on Mathematical Analysis (SIMA). 36, 5, p. 1461-1488 28 p.

Research output: Contribution to journalArticle

7 Citations (Scopus)

Localized periodic patterns for the non-symmetric generalized Swift-Hohenberg equation

Budd, C. J. & Kuske, R., 2005, In : Physica D: Nonlinear Phenomena. 208, 1-2, p. 73-95 23 p.

Research output: Contribution to journalArticle

28 Citations (Scopus)

Multibump, blow-up, self-similar solutions of the complex Ginzburg-Landau equation

Budd, C. J., Rottschafer, V. & Williams, J. F., 2005, In : SIAM Journal on Applied Dynamical Systems. 4, 3, p. 649-678 30 p.

Research output: Contribution to journalArticle

7 Citations (Scopus)

Precise computations of chemotactic collapse using moving mesh methods

Budd, C. J., Carretero-Gonzalez, R. & Russell, R. D., 2005, In : Journal of Computational Physics. 202, 2, p. 463-487 25 p.

Research output: Contribution to journalArticle

40 Citations (Scopus)