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The normal mode model is one of the most popular approaches for solving underwater sound propagation problems. Among other methods, the finite difference method is widely used in classic normal mode programs. In many recent studies, the…
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
The stepwise coupled-mode model is a classic approach for solving range-dependent sound propagation problems. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular generalized eigenvalue problems, which we extend to quasimatrices…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a harmonic point source. Its solution consists of a set of discrete modes radiating into the upper…
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
We show that by using higher order precision arithmetic, i.e., using floating point types with more significant bits than standard double precision numbers, one may accurately compute eigenvalues for non-normal matrices arising in…
We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound…
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range…
A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
Three-dimensional numerical models for underwater sound propagation are popular in computational ocean acoustics. For horizontally slowly varying waveguide environments, an adiabatic mode-parabolic equation hybrid theory can be used for…
An efficient way of solving 2D stability problems in fluid mechanics is to use, after discretization of the equations that cast the problem in the form of a generalized eigenvalue problem, the incomplete Arnoldi-Chebyshev method. This…