TY - JOUR
TI - A note on immersed interface method for three-dimensional elliptic equations
AU - Li, Z.
T2 - Computers & Mathematics with Applications
AB - The Immersed Interface Method proposed by LeVeque and Li [1] is extended to three-dimensional elliptic equations of the form: ∇·(β(x)∇u(x))+κ(x)u(x)=f(x). We study the situation in which there is an irregular interface (surface) S contained in the solution domain across which β, κ and f may be discontinuous or even singular. As a result, the solution u will usually be nonsmooth or even discontinuous. A finite difference approach with a uniform Cartesian grid is used in the discretization. Local truncation error analysis is performed to estimate the accuracy of the numerical solution.
DA - 1996/2//
PY - 1996/2//
DO - 10.1016/0898-1221(95)00202-2
VL - 31
IS - 3
SP - 9-17
J2 - Computers & Mathematics with Applications
LA - en
OP -
SN - 0898-1221
UR - http://dx.doi.org/10.1016/0898-1221(95)00202-2
DB - Crossref
KW - 3D elliptic equation
KW - finite difference methods
KW - irregular interface
KW - discontinuous coefficients
KW - singular source term
KW - delta functions
KW - Cartesian grid
KW - immersed interface method
ER -
TY - JOUR
TI - Robustness studies for H∞ feedback control in a structural acoustic model with periodic excitation
AU - Banks, H. T.
AU - Demetriou, M. A.
AU - Smith, R. C.
T2 - International Journal of Robust and Nonlinear Control
AB - Results from an extensive study on the robustness of an H∞ compensator for a 2-D structural acoustic model are presented. The effects of frequency uncertainties in an exogenous signal are studied for both the case where the signal is contained in the controller formulation and the case where it is excluded. Delays are inserted in the input and/or output signals and their effect on the controller performance is recorded. A comparison between the standard LQG/Kalman filter and the H∞/Min-Max compensator reveals no significant differences in the overall controller performance. Modifications in the controller structure are studied to see whether loss of information (the tracking variable) that must be calculated a priori would result in performance degradation. This study provides valuable insight into the computational and implementational issues that arise when dealing with the control of large and complex systems that are governed by partial differential equations.
DA - 1996/6//
PY - 1996/6//
DO - 10.1002/(sici)1099-1239(199606)6:5<453::aid-rnc222>3.0.co;2-5
VL - 6
IS - 5
SP - 453-478
SN - 1049-8923 1099-1239
UR - http://dx.doi.org/10.1002/(sici)1099-1239(199606)6:5<453::aid-rnc222>3.0.co;2-5
KW - structural/acoustics
KW - H-infinity robust control
KW - computational studies
ER -
TY - CONF
TI - Nonlocal Artificial Boundary Conditions
for Computation of External Viscous Flows
AU - Tsynkov, S. V.
A2 - Desideri, J.-A.
A2 - Hirsch, C.
A2 - Le Tallec, P.
A2 - Pandolfi, M.
A2 - Périaux, J.
C2 - 1996///
C3 - Computational Fluid Dynamics'96.
Proceedings of the Third ECCOMAS CFD Conference,
September 9--13, 1996, Paris, France
CY - Chichester
DA - 1996///
SP - 512-518
PB - John Wiley & Sons
UR - https://www.tib.eu/en/search/id/BLCP%3ACN017470620/Nonlocal-Artificial-Boundary-Conditions-for-Computation/
ER -
TY - RPRT
TI - Artificial Boundary Conditions Based on the Difference Potentials Method
AU - Tsynkov, S. V.
A3 - NASA Langley Research Center
DA - 1996///
PY - 1996///
M1 - NASA-TM-110265, NAS 1.15:110265
PB - NASA Langley Research Center
SN - NASA-TM-110265, NAS 1.15:110265
UR - https://ntrs.nasa.gov/search.jsp?R=19960045440
ER -
TY - JOUR
TI - Use of an Implicit Filtering Algorithm for Mechanical System Parameter Identification
AU - David, J W
AU - Kelley, C T
AU - Cheng, C Y
T2 - 1996 SAE International Congress and Exposition Conference Proceedings, Modeling of CI and SI Engines
DA - 1996///
PY - 1996///
SP - 189-194
ER -
TY - CONF
TI - Consistent Initial Conditions for Unstructured Higher Index {DAE}s: A Computational Study
AU - Campbell, S L
AU - Kelley, C T
AU - Yeomans, K D
C2 - 1996///
C3 - Proceedings of Conference on Computational Engineering in Systems Applications (CESA'96), Lille, France
DA - 1996///
SP - 416-421
ER -
TY - JOUR
TI - An H∞/MinMax Periodic Control in a 2-D Structural Acoustic Model with Piezoceramic Actuators
AU - Banks, H.T.
AU - Demitriou, M.A.
AU - Smith, R.C.
T2 - IEEE Transactions on Automatic Control
AB - A feedback control computational methodology for reducing acoustic sound pressure levels in a two-dimensional cavity with a flexible boundary (a beam) is investigated. The control is implemented in this model through voltages to piezoceramic patches on the beam which are excited in a manner (out-of-phase) so as to produce pure bending moments. The incorporation of the output feedback control in this system leads to a problem with unbounded input and output terms. By writing the resulting system as an abstract Cauchy equation, the problem of reducing interior pressure levels can be posed in the context of an H/sub /spl infin///MinMax time-domain state-space formulation. A summary of extensive computational efforts comparing output feedback to full state feedback and investigating the effect of the number and location of sensors on performance of the control is presented.
DA - 1996/7//
PY - 1996/7//
DO - 10.1109/9.508899
VL - 41
IS - 7
SP - 943-959
SN - 0018-9286
UR - http://dx.doi.org/10.1109/9.508899
ER -
TY - BOOK
TI - Smart Material Structures: Modeling, Estimation and Control
AU - Banks, H.T.
AU - Smith, R.C.
AU - Wang, Y.
DA - 1996///
PY - 1996///
PB - Masson/John Wiley
ER -
TY - JOUR
TI - GMRES and the minimal polynomial
AU - Campbell, S. L.
AU - Ipsen, I. C. F.
AU - Kelley, C. T.
AU - Meyer, C. D.
T2 - BIT Numerical Mathematics
AB - We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size. Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight. Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.
DA - 1996/12//
PY - 1996/12//
DO - 10.1007/bf01733786
VL - 36
IS - 4
SP - 664-675
J2 - Bit Numer Math
LA - en
OP -
SN - 0006-3835 1572-9125
UR - http://dx.doi.org/10.1007/bf01733786
DB - Crossref
KW - GMRES
KW - superlinear convergence
KW - minimal polynomial
KW - eigenvalue index
ER -
TY - JOUR
TI - Existence and uniqueness of solutions of nonlinear systems of conductive-radiative heat transfer equations
AU - Kelley, C. T.
T2 - Transport Theory and Statistical Physics
AB - Abstract We prove an existence and uniqueness results for a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. Our approach uses two different formulations of the system as a compact fixed-point problem. One formulation, which has been used in numerical work, is used for uniqueness and a new one is used for the existence proof.
DA - 1996/3//
PY - 1996/3//
DO - 10.1080/00411459608204839
VL - 25
IS - 2
SP - 249-260
J2 - Transport Theory and Statistical Physics
LA - en
OP -
SN - 0041-1450 1532-2424
UR - http://dx.doi.org/10.1080/00411459608204839
DB - Crossref
ER -
TY - JOUR
TI - Convergence Estimates for Solution of Integral Equations with GMRES
AU - Campbell, S.L.
AU - Ipsen, I.C.F.
AU - Kelley, C.T.
AU - Meyer, C.D.
AU - Xue, Z.Q.
T2 - Journal of Integral Equations and Applications
DA - 1996/3//
PY - 1996/3//
DO - 10.1216/jiea/1181075914
VL - 8
IS - 1
SP - 19-34
J2 - J. Integral Equations Appl.
LA - en
OP -
SN - 0897-3962
UR - http://dx.doi.org/10.1216/jiea/1181075914
DB - Crossref
ER -
TY - JOUR
TI - GMRES and Integral Operators
AU - Kelley, C. T.
AU - Xue, Z. Q.
T2 - SIAM Journal on Scientific Computing
AB - In this paper we show how the properties of integral operators and their approximations are reflected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates by an implicit application of Nyström interpolation, thereby strengthening the norm in which convergence takes place. The smoothed iteration has very similar properties to Broyden’s method. We present an example to illustrate the ideas.
DA - 1996/1//
PY - 1996/1//
DO - 10.1137/0917015
VL - 17
IS - 1
SP - 217-226
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/0917015
DB - Crossref
KW - integral equations
KW - GMRES iteration
KW - Broyden's method
ER -
TY - JOUR
TI - Construction of Artificial Boundary Conditions Using Difference Potentials Method
AU - Tsynkov, S.V.
T2 - Mathematical Modeling
DA - 1996///
PY - 1996///
VL - 8
IS - 9
SP - 118–128
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1444877
ER -
TY - JOUR
TI - Inverse problems in smart material structures
AU - Banks, H. T.
AU - Smith, R. C.
AU - Wang, Y.
T2 - Journal of Inverse and Ill-Posed Problems
DA - 1996///
PY - 1996///
DO - 10.1515/jiip.1996.4.5.371
VL - 4
IS - 5
OP -
SN - 0928-0219 1569-3945
UR - http://dx.doi.org/10.1515/jiip.1996.4.5.371
DB - Crossref
ER -
TY - JOUR
TI - Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions
AU - Banks, H.T.
AU - Smith, R.C.
T2 - Mathematical and Computer Modelling
AB - A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior disturbance by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural flaws through nondestructive evaluation techniques. The presence and excitation of the patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear as a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, well-posedness and approximation results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for system excitation and data collection.
DA - 1996/2//
PY - 1996/2//
DO - 10.1016/0895-7177(96)00002-7
VL - 23
IS - 4
SP - 17-50
J2 - Mathematical and Computer Modelling
LA - en
OP -
SN - 0895-7177
UR - http://dx.doi.org/10.1016/0895-7177(96)00002-7
DB - Crossref
KW - parameter identification
KW - structural acoustics
KW - nonlinear partial differential equations
ER -
TY - JOUR
TI - External flow computations using global boundary conditions
AU - Tsynkov, S. V.
AU - Turkel, E.
AU - Abarbanel, S.
T2 - AIAA Journal
AB - We numerically integrate the compressible Navier-Stokes equations by means of a finite volume technique on the domain exterior to an airfoil. The curvilinear grid we use for discretization of the Navier-Stokes equations is obviously finite, it covers only a certain bounded region around the airfoil, consequently, we need to set some artificial boundary conditions at the external boundary of this region. The artificial boundary conditions we use here are non-local in space. They are constructed specifically for the case of steady-state solution. In constructing the artificial boundary conditions, we linearize the Navier-Stokes equations around the far-field solution and apply the difference potentials method. The resulting global conditions are implemented together with a pseudotime multigrid iteration procedure for achieving the steady state. The main goal of this paper is to describe the numerical procedure itself, therefore, we primarily emphasize the computation of artificial boundary conditions and the combined usage of these artificial boundary conditions and the original algorithm for integrating the Navier-Stokes equations. The underlying theory that justifies the proposed numerical techniques will accordingly be addressed more briefly.
DA - 1996/4//
PY - 1996/4//
DO - 10.2514/3.13130
VL - 34
IS - 4
SP - 700-706
J2 - AIAA Journal
LA - en
OP -
SN - 0001-1452 1533-385X
UR - http://dx.doi.org/10.2514/3.13130
DB - Crossref
ER -