# Multiscale Modeling & Simulation

@inproceedings{BeebeMultiscaleM, title={Multiscale Modeling \& Simulation}, author={Nelson H. F. Beebe} }

Accuracy [Aar04]. Acoustic [VMK05]. Adaptive [JLT04]. Adjoint [CL03b]. Adsorbing [AMK03]. Algebraic [KCH03]. Algorithm [MS04]. Algorithms [BCM05]. Alloys [MR03]. Amplifiers [LM04]. Amplitude [AIL05]. Analysis [CL03a]. Angiogenesis [SWOJ05]. Aperture [FS03]. Application [Fil04]. Applied [SEK05]. Approach [XT04]. Approximation [DSS05]. Approximations [DLY05]. Arbitrary [Str05]. Arteries [CLMT05]. Assimilation [ZG04]. Asymptotic [CD03]. Asymptotics [FPSS03]. Atmospheric [CL03b]. Atomic [LE05b…

## 62 Citations

A Complete Bibliography of Publications in Multiscale Modeling & Simulation

- Mathematics
- 2012

(BV, L) [TNV04]. 1 [BLO17, FG08, VS11]. 1 + 1 [PM14, SPM18, MT09]. 13 [Str05, Tor06]. 2 [AE11, DD13, FFJD09, JR03, VO13, YLY15, Yin15a]. 2 + 1 [BV06, MK06]. 3 [CLLW15, DWC15, LH14, PKC05]. 30…

Variational Stochastic Parameterisations and their Applications to Primitive Equation Models

- Mathematics
- 2022

We present a numerical investigation into the stochastic parameterisations of the Primitive Equations (PE) using the Stochastic Advection by Lie Transport (SALT) and Stochastic Forcing by Lie…

Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media

- MathematicsArXiv
- 2021

A boundary condition is proposed that with overwhelming probability is (near) optimal with respect to scaling in terms of ` and L, in the setting where the medium is a sample from a stationary ensemble with a finite range of dependence.

Fast Huygens' sweeping methods for multiarrival Green's functions of Helmholtz equations in the high-frequency regime

- Geology
- 2015

ABSTRACTMultiarrival Green’s functions are essential in seismic modeling, migration, and inversion. Huygens-Kirchhoff (HK) integrals provide a bridge to integrate locally valid first-arrival Green’s…

Modeling Light Propagation in Luminescent Media in Quality and Form for Publication on Microfilm and Electronically

- Physics
- 2014

OF THE DISSERTATION This study presents physical, computational and analytical modeling approaches for light propagation in luminescent random media. Two different approaches are used, namely (i) a…

Stochastic wave-current interaction in stratified shallow water dynamics

- Environmental Science
- 2019

Holm (Proc. Roy. Soc 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of…

Stochastic circulation dynamics in the ocean mixed layer

- Environmental Science, Physics
- 2020

In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be `thermal'. The thermal rotating shallow…

Solution properties of the incompressible Euler system with rough path advection.

- Mathematics
- 2021

We consider the Euler equations for the incompressible flow of an ideal fluid with an additional rough-in-time, divergence-free, Lie-advecting vector field. In recent work, we have demonstrated that…

Machine learning S-wave scattering phase shifts bypassing the radial Schrödinger equation

- PhysicsThe European Physical Journal B
- 2021

Phase shifts play a key role in partial wave analysis, and are the crucial quantities for obtaining the scattering amplitude by which the elastic scattering properties of the physical or chemical…

will be inserted by hand later ) Polarized Wavelets and Curvelets on the Sphere

- Physics
- 2008

The statistics of the temperature anisotropies in the primordial Cosmic Microwave Background radiation field provide a wealth of information for cosmology and the estimation of cosmological…

## References

SHOWING 1-10 OF 157 REFERENCES

Nonuniform Sampling and Multiscale Computation

- Computer ScienceMultiscale Model. Simul.
- 2014

The goal of this paper is to demonstrate the close relation between and sampling strategies developed in information theory and computational grids in multiscale modeling.

On the Compressive Spectral Method

- Computer ScienceMultiscale Model. Simul.
- 2014

It is shown that the sparse Fourier domain approximation of solutions to multiscale PDE problems by soft thresholding enjoys a number of desirable numerical and analytic properties, including convergence for linear PDEs and a modified equation resulting from the sparse approximation.

A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models

- PhysicsMultiscale Model. Simul.
- 2006

We derive plate theory from atomistic models in the spirit of [G. Friesecke, R. D. James, and S. Muller, Comm. Pure Appl. Math., 55 (2002), pp. 1461–1506] as a Γ‐limit as the number of atoms tends to…

Texture Separation BV-G and BV-L1 Models

- Computer ScienceMultiscale Model. Simul.
- 2007

This work proves a characterization theorem for optimal decompositions for the $BV-L^1$ model, which is the well‐known model of Rudin, Osher, and Fatemi for radial functions.

Time-Reversal Aperture Enhancement

- PhysicsMultiscale Model. Simul.
- 2003

This paper gives a complete analysis of time- reversal of waves emanating from a point source and propagating in a randomly layered medium and shows that random medium fluctuations actually enhance the spatial refocusing around the initial source position.

Multiscale Window Transform

- MathematicsMultiscale Model. Simul.
- 2007

A new analysis apparatus, the multiscale window transform (MWT), is developed to generalize the classical mean-eddy decomposition (MED) in fluid mechanics to include three or more ranges of scales,…

Temporal Regularization of the PN Equations

- MathematicsMultiscale Model. Simul.
- 2009

A regularization of the P_N equations for one-dimensional, slab geometries is introduced, based on a temporal splitting of fast and slow dynamics in the system, to address systems of arbitrary size and with spatially varying media.

Fast Computation of Partial Fourier Transforms

- Computer ScienceMultiscale Model. Simul.
- 2009

Two ecient algorithms for computing the partial Fourier transforms in one and two dimensions are introduced by the wave extrapolation procedure in reection seismology to decompose the summation domain of into simpler components in a multiscale way.

Estimates for the Upscaling Error in Heterogeneous Multiscale Methods for Wave Propagation Problems in Locally Periodic Media

- Computer ScienceMultiscale Model. Simul.
- 2017

The theoretical findings here imply an improved convergence rate in one-dimension, which also justifies the numerical observations from an earlier study, and it is proved that HMM captures the right macroscopic effects.

Wiener Chaos Expansion and Simulation of Electromagnetic Wave Propagation Excited by a Spatially Incoherent Source

- Computer ScienceMultiscale Model. Simul.
- 2009

A new stochastic model for a spatially incoherent source in optical phenomena and a new numerical method based on Wiener chaos expansion (WCE) that is considerably more efficient than the brute-force simulations.