# Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources

@article{Botchev2018ExponentialKT, title={Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources}, author={Mike A. Botchev and Abel M. Hanse and R. Uppu}, journal={J. Comput. Appl. Math.}, year={2018}, volume={340}, pages={474-485} }

## 7 Citations

### 3-D Large-Scale TEM Modeling Using Restarting Polynomial Krylov Method

- Computer ScienceIEEE Transactions on Geoscience and Remote Sensing
- 2022

A restarting polynomial Krylov method is presented for modeling 3-D large-scale TEM responses and it is demonstrated that the method is accurate and uses limited memory.

### A nested Schur complement solver with mesh-independent convergence for the time domain photonics modeling

- Computer ScienceComput. Math. Appl.
- 2020

### A residual concept for Krylov subspace evaluation of the 𝓁 matrix function

- Computer ScienceArXiv
- 2020

An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices, based on a reliable residual based stopping criterion and a new efficient restarting procedure is proposed.

### A residual concept for Krylov subspace evaluation of the $\varphi$ matrix function

- Computer Science
- 2020

Numerical tests demonstrate efficiency of the proposed algorithm for solving large scale evolution problems resulting from discretized in space time-dependent PDEs, in particular, diffusion and convection–diffusion problems.

### An accurate restarting for shift-and-invert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices

- Computer ScienceComputational Mathematics and Mathematical Physics
- 2019

An accurate residual--time (AccuRT) restarting for computing matrix exponential actions of nonsymmetric matrices by the shift-and-invert (SAI) Krylov subspace method is proposed and improved accuracy and efficiency are demonstrated.

### Residual and Restarting in Krylov Subspace Evaluation of the φ Function

- Computer ScienceSIAM J. Sci. Comput.
- 2021

## References

SHOWING 1-10 OF 54 REFERENCES

### Krylov subspace time domain computations of monochromatic sources for multi-frequency optical response

- Computer Science
- 2017

Three different Krylov subspace methods to efficiently solve Maxwell’s equations in a scattering medium for monochromatic sources to calculate a multi-frequency response are presented and two are shown to be efficient and better than the implicit trapezoidal rule (ITR) scheme.

### Krylov subspace exponential time domain solution of Maxwell's equations in photonic crystal modeling

- Computer ScienceJ. Comput. Appl. Math.
- 2016

### Non-invasive imaging through opaque scattering layers

- PhysicsNature
- 2012

An optical method is reported that allows non-invasive imaging of a fluorescent object that is completely hidden behind an opaque scattering layer and can be generalized to other contrast mechanisms and geometries.

### A Krylov Stability-Corrected Coordinate-Stretching Method to Simulate Wave Propagation in Unbounded Domains

- Computer ScienceSIAM J. Sci. Comput.
- 2013

A new Krylov-based solution method via stabilitycorrected operator exponents is presented which allows for reduced-order models (ROMs) that respect the delicate spectral properties of the original scattering problem and outperforms the conventional finitedifference time-domain method for problems on large time intervals.

### Spatiotemporal Coherent Control of Light through a Multiple Scattering Medium with the Multispectral Transmission Matrix.

- PhysicsPhysical review letters
- 2016

This work reports the broadband characterization of the propagation of light through a multiple scattering medium by means of its multispectral transmission matrix and demonstrates spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape.

### Memory effects in propagation of optical waves through disordered media.

- PhysicsPhysical review letters
- 1988

Experimental results generally verify the theoretical predictions of FKLS, but do find one significant difference between experiment and theory — namely, that the exponential decay of C(x) is observed to set in almost immediately with nonzero x, while the theory predicts that its onset should be decelerated.

### Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion

- Physics
- 1999

important corrections are presented. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the ‘‘mesoscopic’’ level and…

### Speckle correlation resolution enhancement of wide-field fluorescence imaging

- Physics
- 2015

High-resolution fluorescence imaging is essential in nanoscience and biological sciences. Due to the diffraction limit, conventional imaging systems can only resolve structures larger than 200 nm.…

### Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods

- Computer Science
- 2015

It is shown how rational Krylov subspace methods may be used to solve the same problem in the frequency domain followed by a synthesis of the transient solution using the fast Hankel transform, arguing that the pure time-domain is more efficient.