A5085592203- Computational Fluid Dynamics and Aerodynamics
- earthquake and tectonic studies
- Advanced Numerical Methods in Computational Mathematics
- Fluid Dynamics and Turbulent Flows
- Seismology and Earthquake Studies
- Gas Dynamics and Kinetic Theory
- Numerical methods for differential equations
- Navier-Stokes equation solutions
- Meteorological Phenomena and Simulations
- Earthquake and Tsunami Effects
- Seismic Imaging and Inversion Techniques
- Electromagnetic Simulation and Numerical Methods
- Matrix Theory and Algorithms
- Lattice Boltzmann Simulation Studies
- Differential Equations and Numerical Methods
- Geophysics and Gravity Measurements
- Methane Hydrates and Related Phenomena
- Advanced Mathematical Modeling in Engineering
- Seismic Waves and Analysis
- Geology and Paleoclimatology Research
- Advanced Mathematical Physics Problems
- Earthquake Detection and Analysis
- Tropical and Extratropical Cyclones Research
- Landslides and related hazards
- Quantum chaos and dynamical systems
Seattle University
2005-2024
University of Washington Applied Physics Laboratory
2015-2024
University of Washington
2012-2024
Tohoku University
2021-2024
Applied Mathematics (United States)
1993-2022
Courant Institute of Mathematical Sciences
1983-2021
New York University
1983-2021
Earth and Space Research
2017-2018
Norwegian Armed Forces
2018
Purdue University West Lafayette
2018
The authors develop finite difference methods for elliptic equations of the form \[ \nabla \cdot (\beta (x)\nabla u(x)) + \kappa (x)u(x) = f(x)\] in a region $\Omega $ one or two space dimensions. It is assumed that simple (e.g., rectangle) and uniform rectangular grid used. situation studied which there an irregular surface $\Gamma codimension 1 contained across $\beta ,\kappa $, f may be discontinuous, along source have delta function singularity. As result, derivatives solution u...
Finite difference approximations -- Steady states and boundary value problems Elliptic equations Iterative methods for sparse linear systems The initial problem ordinary differential Zero-stability convergence Absolute stability Stiff Diffusion parabolic Addiction hyperbolic Mixed Appendixes: A. Measuring errors B. Polynomial interpolation orthogonal polynomials C. Eigenvalues inner-product norms D. Matrix powers exponentials E. Partial equations.
A class of high-resolution algorithms is developed for advection a scalar quantity in given incompressible flow field one, two, or three space dimensions. Multidimensional transport modeled using wave-propagation approach which the flux at each cell interface built up on basis information propagating direction this from neighboring cells. second-order method slope limiters quite easy to implement. For constant flow, minor modification gives third-order accurate method. These methods are...
A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The may consist an elastic boundary immersed in fluid or between two different fluids. represented by cubic spline along which singularly supported surface tension force can be computed. equations are then discretized using finite difference methods elliptic singular sources developed our previous paper [SIAM J. Numer....
The workshop Hyperbolic Conservation Laws , organized by Constantine M. Dafermos (Providence), Dietmar Kröner (Freiburg) and Randall J. LeVeque (Seattle) was held December 7th –13th, 2008. We had 44 participants from eight different countries. atmosphere in the Oberwolfach Research Institute very stimulating has initiated many fruitful discussions exchange of ideas. time schedule as follows: three 30-min-lectures morning afternoon for each lecture at least 15 min discussion. This actively...
Numerical modelling of transoceanic tsunami propagation, together with the detailed inundation small-scale coastal regions, poses a number algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this time-dependent problem in two space dimensions, but even so it is crucial use adaptive mesh refinement order efficiently handle vast differences spatial scales. This must done ‘wellbalanced’ manner that accurately captures very small perturbations steady state...
Abstract Applying probabilistic methods to infrequent but devastating natural events is intrinsically challenging. For tsunami analyses, a suite of geophysical assessments should be in principle evaluated because the different causes generating tsunamis (earthquakes, landslides, volcanic activity, meteorological events, and asteroid impacts) with varying mean recurrence rates. Probabilistic Tsunami Hazard Analyses (PTHAs) are conducted areas world at global, regional, local scales aim...
The method developed in this paper is motivated by Peskin's immersed boundary (IB) method, and allows one to model the motion of flexible membranes or other structures viscous incompressible fluid using a solver on fixed Cartesian grid. IB uses set discrete delta functions spread entire singular force exerted nearby grid points. Our instead incorporates part into jump conditions for pressure, avoiding dipole terms that adversely affect accuracy near boundary. This has been implemented...
Abstract The problem of computing the variance a sample N data points {xi } may be difficult for certain sets, particularly when is large and small. We present survey possible algorithms their round-off error bounds, including some new analysis computations with shifted data. Experimental results confirm these bounds illustrate dangers algorithms. Specific recommendations are made as to which algorithm should used in various contexts. Key Words: VarianceStandard deviationShifted...
We study a general approach to solving conservation laws of the form qt+f(q,x)x=0, where flux function f(q,x) has explicit spatial variation. Finite-volume methods are used in which is discretized spatially, giving fi(q) over ith grid cell and leading generalized Riemann problem between neighboring cells. A high-resolution wave-propagation algorithm defined waves based directly on decomposition differences fi(Qi-1(Qi-1 ) into eigenvectors an approximate Jacobian matrix. This method shown be...
An adaptive mesh refinement algorithm developed for the Euler equations of gas dynamics has been extended to employ high-resolution wave-propagation algorithms in a more general framework. This allows its use on variety new problems, including hyperbolic not conservation form, problems with source terms or capacity functions, and logically rectangular curvilinear grids. framework requires modified approach maintaining consistency at grid interfaces, which is described detail. The implemented...
Numerical methods are studied for the one-dimensional heat equation with a singular forcing term, $u_t = u_{xx} + c(t)\delta (x - \alpha (t)).$ The delta function $\delta (x)$ is replaced by discrete approximation $d_h and resulting solved Crank–Nicolson method on uniform grid. accuracy of this analyzed various choices $. case where $c(t)$ specified also c determined implicitly constraint solution at point studied. These problems serve as model immersed boundary Peskin incompressible flow in...
We show that any conservative scheme for solving scalar conservation laws in two space dimensions, which is total variation diminishing, at most first-order accurate.