Browsing Computational and Applied Mathematics by Title
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The PlaneWave Detection Problem
(199208)The planewave detection problem is: to estimate the incidence angle and waveform of a transient plane traveling wave, from samples recorded at a linear array of receivers. This simple problem shares several important ... 
The Rate at Which Energy Decays in a String Damped at One End
(199501)The energy in a nonhomogeneous string that moves freely at one end and against unit friction at the other is known to decay exponentially in time. The energy in fact vanishes in finite time when the string's density is ... 
The Reflection Inverse Problem for Acoustic Waves
(199012)We study an acoustic model of the inverse problem of reflection seismology. A straightforward bestfit formulation of this problem has been used by several investigators as the basis for numerical solution of this problem, ... 
The Secant/Finite Difference Alogorithm for Solving Sparse Nonlinear Systems of Equations
(198603)This paper presents an algorithm, the secant/finite difference algorithm, for solving sparse nonlinear systems of equations. This algorithm is a combination of a finite difference method and a secant method. A qsuperlinear ... 
The Solution of the Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method
(199412)This paper considers numerical algorithms for finding local minimizers of metric multidimensional scaling problems. The two most common optimality criteria (STRESS and SSTRESS) are considered, the leading algorithms for ... 
The Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming
(199904)We study a local feature of a Newton logarithmic barrier function method and a Newton primaldual interiorpoint method. In particular, we study the radius of the sphere of convergence of Newton's method on two equivalent ... 
The Stability of GMRES Convergence, with Application to Approximate Deflation Preconditioning
(201109)How does GMRES convergence change when the coefficient matrix is perturbed? Using spectral perturbation theory and resolvent estimates, we develop simple, general bounds that quantify the lag in convergence such a perturbation ... 
The Standard Vector Library: a software framework for coupling complex simulation and optimization
(200409)Object oriented design solves a fundamental programming problem arising in simulation driven optimization: the separation in code of multiple levels of abstraction naturally appearing in solution algorithms for such problems. ... 
The Steepest Descent Minimization of DoubleWell Stored Energies Does Not Yield Vectorial Microstructures
(200103)We prove that the Steepest Descent algorithm applied to the minimization of total stored energies with rankone related rotationally symmetric energy wells does not produce relaxing vectorial microstructures with nontrivial ... 
The Total Variation Regularized L1 Model for Multiscale Decomposition
(200611)This paper studies the total variation regularization model with an L1 fidelity term (TVL1) for decomposing an image into features of different scales. We first show that the images produced by this model can be formed ... 
The Two Phase Drum with the Deepest Bass Note
(199010) 
The Use of Optimization Techniques in the Solution of Partial Differential Equations
(199604)Optimal Control of systems governed by Partial Differential Equations is an applicationsdriven area of mathematics involving the formulation and solution of minimization problems. Given a physical phenomenon described by ... 
Thermal Simulation of Pipeline Flow
(199109)A new numerical method for studying one dimensional fluid flow through pipelines is presented and analyzed. This work extends in a certain direction the collocation method described by Luskin ["An Approximation Procedure ... 
Three Dimensional Simulation of Steam Displacement with Minimal Grid Orientation
(198303)Steamflooding is a tertiary oil recovery mechanism with proven economic potential. Reliable numerical simulations of candidate injection schemes can aid in the optimization of process parameters. Stateoftheart numerical ... 
ThreeDimensional Bioremediation Modeling in Heterogeneous Porous Media
(199204)Recently Rice University and Pacific Northwest Laboratory (PNL) have begun a collaborative research effort that involves laboratory, field, and simulation work directed toward validating remediation strategies, including ... 
TimeDependent Coupling of NavierStokes and Darcy Flows
(201109)A weak solution of the coupling of timedependent NavierStokes equations with Darcy equations is defined. The interface conditions include the BeaversJosephSaffman condition. Existence and uniqueness of the weak solution ... 
TimeDependent Coupling of NavierStokes and Darcy Flows
(2013)A weak solution of the coupling of timedependent incompressible NavierﾖStokes equations with Darcy equations is defined. The interface conditions include the BeaversﾖJosephﾖSaffman condition. Existence and uniqueness of ... 
TimeDomain Decomposition Preconditioners for the Solution of Discretized Parabolic Optimal Control Problems
(200603)Optimal control problems governed by timedependent partial differential equations (PDEs) lead to largescale optimization problems. While a single PDE can be solved by marching forward in time, the optimality system for ...