Related papers: A conservative adaptive wavelet method for the sha…
This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…
We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal & Kupferman (2004,2005} combined with the…
Fourier extension is an approximation method that alleviates the periodicity requirements of Fourier series and avoids the Gibbs phenomenon when approximating functions. We describe a similar extension approach using regular wavelet bases…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We introduce a novel weather-adaptive approach for multi-step forecasting of multi-scale SOP changes in aerial fiber links. By harnessing the discrete wavelet transform and incorporating weather data, our approach improves forecasting…
We develop a conservative phase-space grid-adaptivity strategy for the Vlasov-Fokker-Planck equation in a planar geometry. The velocity-space grid is normalized to the thermal speed and shifted by the bulk-fluid velocity. The…
Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a…
Efficient time series forecasting is essential for smart energy systems, enabling accurate predictions of energy demand, renewable resource availability, and grid stability. However, the growing volume of high-frequency data from sensors…
We present an adaptive wavelet Galerkin method for transient heat conduction in heterogeneous composite materials. The approach combines multiresolution wavelet bases with an implicit time discretization to efficiently resolve sharp…
New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrary to classical wavelet transforms, the algorithms are not based on filter coefficients, but on algorithms for B-spline…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
The development of surrogate models to study uncertainties in hydrologic systems requires significant effort in the development of sampling strategies and forward model simulations. Furthermore, in applications where prediction time is…
Real-time water-level monitoring across many locations is vital for flood response, infrastructure management, and environmental forecasting. Yet many sensing methods rely on fixed instruments - acoustic, radar, camera, or pressure probes -…
This paper enhances the classic Smagorinsky model by introducing an innovative, adaptive dissipation term that adjusts dynamically with distance from boundary regions. This modification addresses a known limitation of the standard model…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
An adaptive sampling approach for efficient detection of bifurcation boundaries in parametrized fluid flow problems is presented herein. The study extends the machine-learning approach of Silvester~(J. Comput. Phys., 553 (2026), 114743),…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns…