Applied Mathematics, Department of
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Applied Mathematics is the discipline of discovering, applying, and promoting the use of mathematics to model and solve practical problems in many disciplines, ranging from physical sciences and biology to medicine and business. By exploiting the common underlying mathematical framework, the Department of Applied Mathematics initiates the crossfertilization of ideas and techniques from one discipline to another. Many of our faculty members are either joint or adjunct faculty in another department. The faculty is widely known for its research leadership and authorship of many research papers, textbooks, and monographs, and activity on editorial boards of leading journals.
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Developing a Warning System for Inbound Tsunamis from the Cascadia Subduction Zone
(20180107)Realtime tsunami warning in the nearfield is considerably more difficult than producing warnings for distant events. Although in some cases strong shaking will provide the only warning, there are several situations in ... 
GeoClaw Model Tsunamis Compared to Tide Gauge Results Final Report
(20181103)The purpose of this project is to compare GeoClaw tsunami model results to detided tide gauge results at multiple destinations for each of several tsunamis. In particular, we are interested in the suitability of GeoClaw ... 
Tsunami Hazard Assessment of the Strait of Juan de Fuca
(20150924)This report documents the results of a study supported by the Washington State Emergency Management Division of the tsunami hazard along the Strait of Juan de Fuca. Results include inundation depths and times of arrival ... 
Probabilistic Tsunami Hazard Assessment (PTHA) for Crescent City, CA. Final Report for Phase I
(University of Washington Department of Applied Mathmatics, 20130202)This demonstration Probabilistic Tsunami Hazard Assessment (PTHA) study of Crescent City, California was funded by BakerAECOM and motivated by FEMA's desire to explore methods to improve products of the FEMA Risk Mapping, ... 
Finite volume methods and adaptive refinement for global tsunami propagation and local inundation
(2006)The shallow water equations are a commonly accepted approximation governing tsunami propagation. Numerically capturing certain features of local tsunami inundation requires solving these equations in their physically ... 
Highresolution finite volume methods for dusty gas jets and plumes
(2006)We consider a model for dusty gas flow that consists of the compressible Euler equations for the gas coupled to a similar (but pressureless) system of equations for the mass, momentum, and energy of the dust. These sets ... 
CORRECTION TO THE ARTICLE A COMPARISON OF THE EXTENDED FINITE ELEMENT METHOD WITH THE IMMERSED INTERFACE METHOD FOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND SINGULAR SOURCES BY VAUGHAN ET AL.
(2008)A recent paper by Vaughan, Smith, and Chopp [Comm. App. Math. &and Comp. Sci. 1 (2006), 207–228] reported numerical results for three examples using the immersed interface method (IIM) and the extended finite element method ... 
Highresolution rotated grid method for conservation laws with embedded geometries
(2005)We develop a secondorder rotated grid method for the approximation of time dependent solutions of conservation laws in complex geometry using an underlying Cartesian grid. Stability for time steps adequate for the ... 
A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions
(Society for Industrial and Applied Mathematics, 2002)We study a general approach to solving conservation laws of the form qt+f(q,x)x=0, where the flux function f(q,x) has explicit spatial variation. Finitevolume methods are used in which the flux is discretized spatially, ... 
A class of approximate Riemann Solvers and their relation to relaxation schemes
(Elsevier/Academic Press, 20010930)We show that a simple relaxation scheme of the type proposed by Jin and Xin [Comm. Pure Appl. Math.48, 235 (1995)] can be reinterpreted as defining a particular approximate Riemann solver for the original system of m ... 
A wave propagation method for threedimensional hyperbolic conservation laws
(Elsevier, 20001120)A class of wave propagation algorithms for threedimensional conservation laws and other hyperbolic systems is developed. These unsplit finitevolume methods are based on solving onedimensional Riemann problems at the ... 
A wave propagation algorithm for hyperbolic systems on curved manifolds
(Elsevier, 20040920)An extension of the wave propagation algorithm first introduced by LeVeque [J. Comput. Phys. 131 (1997) 327] is developed for hyperbolic systems on a general curved manifold. This extension is important in a variety of ...