List of Main Publications of J. J. H. Miller
RESEARCH MONOGRAPHS
1. “New tools in
computational fluid dynamics for aerospace engineering”.(J
J H Miller) Global Aerospace Technology, Business
Briefing, World Markets Series, World Markets Research Centre (2000) 70-72.
1. "Matrix
theorems for partial differential and difference equations" (with
2. "On
power-bounded operators, and operators satisfying a resolvent
condition" Numer. Math. 10 (1967) 389-396.
3. "On the resolvent of a linear operator associated with a well-posed
Cauchy problem" Math. Comp. 20 (1968) 541-548.
4. "The
construction of unbalanced difference operators for parabolic initial-boundary
value Problems" S.I.A.M. J. on Numer. Anal. 6
(1969) 476-479.
5. "Radial
limits of the rational functions of Harish-Chandra"
(with D.J. Simms). Proc. Roy. Irish
Acad. 68 (1969) 41-47.
6. "A
difference equation satisfied by the functions of Harish-Chandra"
(with D.J. Simms). Amer. J. Math. 92
(1970) 362-367.
7. "On the
location of zeros of certain classes of polynomials with applications to
numerical analysis" J. Inst. Math. Applic. 8
(1971) 397-406.
8. "On weak
stability, stability and the type of a polynomial" Lecture Notes in
Mathematics, Vol. 228. Conference on
Application of Numerical Analysis, Ed. John L. Morris. Springer Verlag
(1971) 316-320.
9. "On the
stability of differential equations" S.I.A.M. J. Control. 10 (1972)
639-648.
10. "The
refinement and implementation of an algorithm for finding the type of a
polynomial" (with D.P. McCarthy). Seminaires Analyse Numerique
1972-1973, Eds. J.L. Lions, P.A. Raviart, Universite Paris VI, 1-9.
11. "On the
coefficients of an asymptotic expansion of spherical functions on symmetric
spaces" (with D.J. Simms). Proc.
Amer. Math. Soc. 37 (1973) 448-452.
12. "On the
differential equation for spherical functions on certain symmetric spaces"
(with D.J. Simms). Proc. Roy. Irish
Acad. 73 A (1973) 19-24.
13. "Practical
algorithms for finding the type of a polynomial" Studies in Numerical
Analysis, Ed. B.K.P. Scaife. Academic Press,
14. "On the type
of a polynomial relative to a line - a special case" Proceedings of the
Conference Numerische Methoden
bei Optimierungsaufgaben. Band 2, Eds. L. Collatz,
W. Wetterling.
ISNM, Vol. 23, Birkhäuser Verlag
(1974) 101-112.
15. "On the type
of a polynomial f when f*(0)f - f(0)f* is a
monomial" Computers and Mathematics with Applications 1 (1975) 299-306.
16. "The
stability properties of q-step backward difference schemes" (with David Creedon). BIT 15
(1975) 244-249.
17. "On the type
of a polynomial relative to a circle - an open problem" Optimization Techniques
I.F.I.P. Technical Conference,
18. "Construction
of a FEM for a singularly perturbed problem in 2 dimensions" Proceedings of
the Conference: Numerische Behandlung
von Differential-gleichungen, insbesondere
mit der Methode
der finiten Elemente. Oberwolfach, November 1975, ISNM, Vol. 31, Birkhauser Verlag (1976) 165-169.
19. "A finite
element method for a two point boundary value problem with a small parameter
affecting the highest derivative" Proceedings of the 5th Semester:
Mathematical Models and Numerical Methods.
Stefan Banach, International Mathematical Center,
20. "Sufficient
conditions for the convergence, uniformly in e, of a three
point difference scheme for a singular perturbation problem" in Numerical
Treatment of Differential Equations in Applications, Proc. of Conf. at Oberwolfach, 11-17 December 1977. Lecture Notes in Mathematics No. 679,
Springer-Verlag (1978) 85-91.
21. "On the
convergence uniformly in e, of difference schemes for
a two point boundary singular perturbation problem" in Numerical Analysis
of Singular Perturbation Problems, Eds. J.J.H. Miller, P.W. Hemker.
Academic Press (1978) 467-474.
22. "Some finite
difference schemes for a singular perturbation problem" in Constructive
Function Theory, Proc. of the Int. Conf. on Constructive Function Theory, Blagoevgrad 30 May - 4 June 1977, Sofia (1980) 399-402.
23. "Hinged
finite element methods for two point boundary value problems with a singular
perturbation" (with E. O'Riordan). Numerical Methods in Continuum Mechanics,
Vol. 14 No. 2 (1983) 142-154.
24. "Large
numbers on small computers" (with A.A. Sloane) in Proc. IFIP and TC2
Working Conference on PDE Software: Modules, Interfaces and Systems,
25. "A
correction term for the Scharfetter-Gummel finite
difference scheme"
BAIL III Procs. 3rd International Conf.
on Boundary and Interior Layers, Boole Press,
26. "A new
treatment of the recombination term in the current continuity equations of
semiconductor device models" Engineering Computations, Vol. 2 No. 1 (1985)
71-73.
27. "Petrov-Galerkin finite element methods with a hinged test
space for singularly perturbed problems" (with C. Fitzsimons, E. O'Riordan).
International Journal for Numerical Methods in Engineering, Vol. 21
(1985) 1803-1812.
28. "The rise of
information technology and its significance for mathematics" in Computers
and Mathematics in the Modern Society, Proc. of Workshop held October
31-November 1, 1983, Benin City, Nigeria.
Ed. S.O. Fatunla. Macmillan
29. "On the
design of numerical methods for modelling semiconductor devices" Invited
paper at the First International Conference on Computational Mathematics held
at
30. "Optimal
uniform difference schemes for linear initial value problems" Computers
and Mathematics with Applications, Vol. 12B No. 5/6 (1986) 1209-1215.
31. "On the
inclusion of the recombination term in discretisations
of the semiconductor device equations" Mathematics and Computers in
Simulation, Vol. 28 (1986) 1-11.
32. "On the discretisation of the semiconductor device equations in the
two dimensional case" Invited paper at the Second International Conference
on Computational Mathematics held at University of Benin, Benin City, Nigeria,
29-31 January 1986. Computational Mathematics II, Boole
Press,
33. "On a Petrov-Galerkin method for the electrical and thermal
behaviour of semiconductor devices in two dimensions" Mathematics and
Computers in Simulation, Vol. 29 (1987) 367-372.
34. "Some
numerical techniques for the solution of problems related to semiconductor
devices" in Numerical Approximation of Partial Differential Equations,
Proceedings of the International Symposium of Numerical Analysis, Madrid,
September 17-19, (1985). Ed. E.L. Ortiz,
35. "A mixed
finite element method for the stationary semiconductor continuity
equations" (with
36. "Mixed
finite element methods for the semiconductor device equations" ISNM, Vol.
86 Birkhaeuser Verlag,
37. "Petrov-Galerkin and Green's function methods for nonlinear
boundary value problems with applications to semiconductor devices" (with
I.P. Boglaev). Proc. Roy. Irish Acad., Vol. 88A No. 2
(1988) 153-168.
38. "A Petrov-Galerkin mixed finite element method with triangular
elements for the semiconductor device equations" (with
39. "Mixed
finite element methods for semiconductor device equations" (with
40. "Hexahedral
finite elements for the stationary semiconductor device equations" (with
C.J. Fitzsimons,
41. "A mixed
finite element method with tetrahedral elements for the semiconductor
continuity equations" (with
42. "An ¶-uniformly convergent
non-conforming finite element method for a singularly perturbed elliptic
problem in two dimensions" (with
43. "A
triangular mixed finite element method for the stationary semiconductor device
equations" (with
44. "A simple
recipe for uniformly convergent finite difference schemes for singularly
perturbed problems" (with
45. "On the
construction of uniformly convergent finite difference schemes for singularly
perturbed problems for a quasilinear elliptic
equation" (with G.I. Shishkin). Computational Methods for Boundary and
Interior Layers in Several Dimensions, ed. J.J.H. Miller, Boole
Press,
46. "An exponentially
fitted finite element method for a stationary convection - diffusion
problem" (with
47. "Iterative
and Petrov-Galerkin methods for a nonlinear two-point boundary value
problems with application to semiconductor devices" (with B.Y. Guo). Numerical
Methods for Partial Differential Equations.
Eds. Y. Lungan, Guo Benyu, World Scientific,
48. "Iterative
and finite difference methods for solving a system of nonlinear elliptic
equations" (with B.Y. Guo). Journal of Applied
Sciences, Vol. 10 No. 1 (1992) 1-24.
49. "Iterative
and Petrov-Galerkin methods for solving a system of
one-dimensional nonlinear elliptic equations" (with B.Y. Guo). Mathematics of
Computation, Vol. 58 No. 198 (1992) 531-547.
50. "A second
order L-stable time discretisation of the
semiconductor device equations" (with C.J. Fitzsimons, F. Liu). Journal of Computational and Applied
Mathematics, 42 (1992) 175-186.
51. "Inverse
average type finite element schemes for the stationary semiconductor device
equations" (with Liu Fawang). J. Computational and Applied Maths 44 (1992)
77-94.
52. "Numerical
results for a convection-diffusion problem with a non-slip condition"
(with A. Hegarty, E. O'Riordan,
G.I. Shishkin).
BAIL VI Procs. 6th International Conf on
Boundary and Interior Layers.
53. "Special
finite difference methods for calculating heat fields in solid bodies with
rapidly changing surface temperature" (with E. O'Riordan,
E.A. Petrenko, G.I. Shishkin). Applications of Computational Methods for
Boundary and Interior Layers, ed. J.J.H. Miller, Boole
Press,
54. "Key to the
computation of the transfer of a substance by convection-diffusion in a laminar
fluid" (with A.F. Hegarty, E. O'Riordan, G.I. Shishkin). Applications of Computational Methods for
Boundary and Interior Layers, ed. J.J.H. Miller, Boole
Press,
55. "An e-uniformly convergent finite
box method for a singularly perturbed advection-diffusion equation" (with
56. "The
numerical solution of a moving boundary problem in two dimensions with
applications to drug delivery systems" (with L.J. Crane, P.B. Deasy, E.M. Kenny).
Modelling in Mechanics, Tom 7 (24) No. 2 (1993) 124-132.
57. "A
tetrahedral mixed finite element method for the stationary semiconductor
continuity equations" (with
58. "A new
non-conforming Petrov-Galerkin finite element method
with triangular elements for a singularly perturbed advection-diffusion
problem" (with
59. "An
exponentially fitted finite volume method for the numerical solution of 2-d
unsteady incompressible flow problems" (with S. Wang,). Journal of Computational Physics 115, 1, (1994)
56-64.
60. "Use of
central difference operators for the solution of singularly perturbed
problems" (with A. Hegarty, E. O'Riordan, G.I. Shishkin). Comms. Appl. Numer. Methods, Vol. 10
(1994) 297-302.
61. "An analysis
of the Scharfetter-Gummel box method for the
stationary semiconductor device equations" (with S. Wang). Modélisation Mathématique et Analyse Numérique, M2AN, Vol. 28 No. 2 (1994) 123-140.
62. "Special
numerical methods for convection-dominated laminar flows at arbitrary Reynolds
number" (with A. Hegarty, E. O'Riordan,
G.I. Shishkin).
East-West Journal of Numerical Methods, 2, (1994) 65-74.
63. "On
numerical experiments with central difference operators on special piecewise
uniform meshes for problems with boundary layers" (with A.F. Hegarty, E. O'Riordan, G.I. Shishkin). Procs. 9th GAMM-Seminar Kiel, Jan 22-24, (1993) Vol. 46,
Notes on Numerical Fluid Mechanics, Vieweg-Verlag,
(1994) 167-176.
64. "Erosion of
an infinite cylinder" (with L.J. Crane, P.B. Deasy,
E.M. Kenny). Z. Angew.
Math. Mech., 74, (1994) 633-635.
65. "On the
implementation of a 3D semiconductor device simulator on distributed-memory MIMD/SIMD
machines" (with
66. "Computational
tools for interpolations and curve fitting under uncertainties" (with Y. Akyildiz, S. Markov, E. Popova). Proc. of the 2nd Hellenic European Conf. on
Mathematics and Informatics, Hermis '94, 22-24
September 1994, Athens, (1994) 659-666.
67. "Special
meshes for finite difference approximations to an advection-diffusion equation
with parabolic layers" (with A.F. Hegarty, E. O'Riordan, G.I. Shishkin). Journal of Computational Physics 117, (1995)
47-54.
68. "On a novel
mesh for the regular boundary layers arising in advection-dominated transport
in two dimensions" (with A.F. Hegarty, E. O'Riordan, G.I. Shishkin). Comms. in Numer. Methods in Engineering,
Vol. 11 (1995) 435-441.
69. "Uniform
convergence of arbitrary order on non-uniform meshes for a singularly perturbed
boundary value problem" (with C. Clavero, F. Lisbona). J.
Computational and Applied Maths., 59 (1995) 155-171.
70. "On
piecewise-uniform meshes for upwind and central difference operators for
solving singularly perturbed problems" (with E. O'Riordan,
G.I. Shishkin).
IMA J. Numer. Anal., 15 (1995) 89-99.
71. "On the
design of piecewise uniform meshes for solving advection-dominated transport
equations to a prescribed accuracy" (with P.A. Farrell, A.F. Hegarty, E. O'Riordan, G.I. Shishkin). Notes on Numerical Fluid Mechanics, Vieweg-Verlag, Vol. 49, (1995) 86-95.
72. "Numerical
results for advection-dominated heat transfer in a moving fluid with a non-slip
boundary condition" (with A.F. Hegarty, E. O'Riordan, G.I. Shishkin). Intl. J. Numer. Meth. Heat & Fluid Flow, Vol. 5 No. 2 (1995) 131-140.
73. "The effect
of riblets in stagnation point flow" (with N.
Bach, L.J. Crane). Z. Angew. Math. Mech., 75, (1995) 377-378.
74. "A uniformly
convergent finite difference scheme for a singularly perturbed semilinear equation" (with P. Farrell, E. O'Riordan, G.I. Shishkin). SIAM JNA 33 (3) (1996) 1135-1149.
75. "On the use
of fitted operator methods for singularly perturbed partial differential
equations" (with E. O'Riordan, G.I. Shishkin) Proceedings of International Conference on
Advanced Mathematics, Computations and Applications AMCA-95,
76. "Convergence
of the nonconforming Wilson's brick for arbitrary hexahedral meshes" (with
77. "Analysis of
Rayleigh-Lamb wave scattering by a crack in an
elastic plate" (with L.J. Crane, M.D. Gilchrist) Computational Mechanics
19, 6 (1997) 533-537.
78. "Fitted mesh
methods for the singularly perturbed reaction diffusion problem" (with E. O'Riordan, G.I. Shishkin) Proc.
Fifth International Colloquium on Numerical Analysis, Plovdiv,
Bulgaria August 1996, Ed. E. Minchev, Academic Publ. (1997) 99-105.
79. “The necessity of
fitted operators and Shishkin meshes for resolving
thin layer phenomena” (with E O’Riordan) CWI
Quarterly, 10, 3&4, (1997) 207-213.
80. "Numerical
solution of elliptic convection-diffusion problems on fitted meshes" (with
A. F. Hegarty, E O’Riordan,
G I Shishkin) CWI Quarterly, 10, 3&4, (1997)
239-251.
81. "An accurate
numerical solution of a two dimensional heat transfer problem with a parabolic
boundary layer" (with C. Clavero, E. O'Riordan, G.I. Shishkin). J. Computational Maths. 16, 1, (1998) 27-39.
82. "On the
non-existence of e-uniform finite difference methods on uniform meshes for semilinear two point boundary value problems" (with P.
Farrell, E. O'Riordan, G.I. Shishkin)
Math. Comp. 67, 222 (1998) 603-617.
83. "Fitted
numerical methods for four simple convection-diffusion problems" (with E. O'Riordan, G.I. Shishkin). Procs. 2nd Asian
Maths. Conf., Thailand 1995. Eds. S. Tangmanee &
E. Schultz, World Scientific Publishing Co., Singapore, New Jersey, Hong Kong
(1998) 444-448.
84. "Fitted mesh
methods for problems with parabolic boundary layers" (with E. O'Riordan, G.I. Shishkin, L.P. Shishkina) Math. Proc. Roy. Irish Acad. Vol. 98A,
No. 2, (1998)
173-190.
85. "Application
of finite element methods to the simulation of semiconductor devices"
(with W.H.A. Schilders, S. Wang) Reports on Progress
in Physics, 62, 3 (1999) 277-353 .
86. "On a fitted
operator technique for singular perturbation equations" (with P.A.
Farrell, A.Hegarty, E. O'Riordan,
G. I. Shishkin) in Finite Difference methods: Theory
and Applications, Eds. A.A. Samarskii, L. G. Vulkov, P. N. Vabishchevich, Nova Science Books, New York. (1999) 71-78.
87. "A
parameter-uniform Schwarz method for a singularly perturbed reaction-diffusion
problem with an interior layer” (with E. O'Riordan,
G.I. Shishkin, S. Wang) Applied Numerical Maths., 35
(2000) 323-337.
88. "Singularly perturbed
differential equations with discontinuous source terms" (with P Farrell, E O’Riordan,
G I Shishkin) in Analytical and Numerical Methods for
Convection-Dominated and Singularly Perturbed Problems, (Eds. L.G. Vulkov, J.J.H. Miller, G.I. Shishkin),
Nova Science Publishers, New York. (2000) 23-31.
89. "Schwarz
iterative method for convection-diffusion problems with boundary layers"
(with H. MacMullen E. O'Riordan,
G.I. Shishkin) in Analytical and Numerical Methods
for Convection-Dominated and Singularly Perturbed Problems, (Eds. L.G. Vulkov, J.J.H. Miller, G.I. Shishkin),
Nova Science Publishers, New York. (2000) 213-218.
90. "A parameter
robust numerical method for a system of singularly perturbed ordinary
differential equations" (with S. Matthews, E. O'Riordan,
G.I. Shishkin)
in Analytical and Numerical Methods for Convection-Dominated and
Singularly Perturbed Problems, (Eds. L.G. Vulkov,
J.J.H. Miller, G.I. Shishkin), Nova Science
Publishers, New York. (2000) 219-224.
91. “Accurate
numerical method for Blasius' problem for flow past a
flat plate with mass transfer” (with B. Gahan, G.I. Shishkin) in Finite Difference Schemes, (Eds. R. Ciegis, A. Samarskii, M. Sapagovas) Institute of Mathematics and Informatics,
Vilnius (2000) 63-74.
92. “On
Reynolds-uniform numerical methods, in parabolic boundary layer regions, for Prandtl’s problems” (with G.I. Shishkin,
P.A. Farrell, A.F. Hegarty, E. O'Riordan)
in Finite Difference Schemes, (Eds. R. Ciegis, A. Samarskii, M. Sapagovas)
Institute of Mathematics and Informatics, Vilnius (2000) 215-225.
93. “Parameter-uniform
numerical methods for a class of singularly perturbed problems with a Neumann
boundary condition” (with P.A. Farrell, A.F. Hegarty,
E. O'Riordan and G.I. Shishkin)
in Numerical Analysis and Its Applications (Eds. L. Vulkov,
J. Wasniewski, P. Yamalov),
Lecture Notes in Computer Science, 1988, Springer (2001) 292-303.
94. “Reynolds--uniform
numerical method for Prandtl's problem with
suction--blowing based on Blasius' approach” (with B.
Gahan, G.I. Shishkin) in
Numerical Analysis and Its Applications (Eds. L. Vulkov,
J. Wasniewski, P. Yamalov),
Lecture Notes in Computer Science, 1988, Springer (2001) 304-315.
95. “A robust
layer-resolving numerical method for plane stagnation point flow” (with A.
Musgrave, G.I. Shishkin) in Numerical Analysis and
Its Applications (Eds. L. Vulkov, J. Wasniewski, P. Yamalov), Lecture
Notes in Computer Science, 1988, Springer (2001) 594-601.
96. “On a necessary
requirement for Re-uniform numerical methods to solve boundary layer equations
for flow along a flat plate” (with G.I. Shishkin,
P.A. Farrell, A.F. Hegarty, E. O'Riordan)
in Numerical Analysis and Its Applications (Eds. L. Vulkov,
J. Wasniewski, P. Yamalov),
Lecture Notes in Computer Science No. 1988, Springer (2001) 723-731.
97. "A second
order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with
boundary layers" (with H. MacMullen, E. O'Riordan, G.I. Shishkin) J.
Comp. Appl. Math., 130, 1-2 (2001) 231-244.
98. "Numerical
experiments for advection-diffusion problems in a channel with a 180 degree
bend" (with C. Clavero, E. O'Riordan,
G.I. Shishkin) Applied Mathematics and Computation,
118, 2-3 (2001) 223-246.
99. “A robust
layer-resolving numerical method for a free convection problem” (with J.Étienne, G.I. Shishkin) in Mathematics
in the 21st century (Eds. A.A. Ashour,
A.-S.F. Obada) World Scientific (2001) 189-198.
100. “A parameter-uniform fitted mesh method for
quasilinear differential equations with boundary layers” (with P.A.
Farrell, E. O'Riordan, G.I. Shishkin)
Computational Methods in Applied Mathematics, 1, 2 (2001) 154-172.
101. “An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number” (with P.A. Farrell, A.F. Hegarty, E. O'Riordan, G.I. Shishkin). Applied Numerical Mathematics, 40, 1-4 (2002) 143-149.
102. “A Reynolds--Uniform
Numerical Method for Prandtl's Boundary Layer Problem
for Flow Past a Plate with Mass Transfer”(with J.S.
Butler, G I Shishkin) in Recent Advances in Computational Science & Engineering Eds. H P Lee, K Kumar, Procs. Intl. Conf. on Sci. &
Eng. Comp.,
103. “A Reynolds-uniform
numerical method for Prandtl's boundary layer problem
for flow past a wedge” (with J.S. Butler, G.I. Shishkin),
International Journal for Numerical Methods in Fluids, 43, (2003) 903-913.
104. “Computing realistic Reynolds-uniform
error bounds for discrete derivatives of flow velocities in the boundary layer
for Prandtl's problem” (with P.A. Farrell, A.F. Hegarty, E. O'Riordan, G.I. Shishkin), International Journal for Numerical Methods in
Fluids, 43, (2003) 895-902.
105. “Numerical techniques for
flow problems with singularities” (with P.A. Farrell, A.F. Hegarty,
E. O'Riordan, G.I. Shishkin),
International Journal for Numerical Methods in Fluids, 43, (2003) 915-936.
106. “A Reynolds-uniform
numerical method for the Prandtl solution and its
derivatives for stagnation line flow” (with A.P. Musgrave, G.I. Shishkin), International Journal for Numerical Methods in
Fluids, 43, (2003) 881-894.
107. “Singularly perturbed
convection diffusion problems with boundary and weak interior layers” (with
P.A. Farrell, A.F. Hegarty, E. O'Riordan,
G.I. Shishkin) Journal of Computational and Applied
Mathematics (in press).
108. “Grid approximation of a
singularly perturbed boundary value problem modelling
heat transfer in the case of flow over a flat plate with suction of the
boundary layer” (with G.I. Shishkin, B. Koren, L.P. Shishkina) Journal of
Computational and Applied Mathematics (in press).