Publication
MATHICSE Technical Report : Function integration, reconstruction and approximation using rank-1 lattices
Related publications (51)
Verification of the Fourier-enhanced 3D finite element Poisson solver of the gyrokinetic full-f code PICLS
Laurent Villard, Stephan Brunner, Alberto Bottino, Moahan Murugappan
We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily paralle ...
Elsevier2024An optimal preconditioned FFT-accelerated finite element solver for homogenization
Till Junge, Ali Falsafi, Martin Ladecký
We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...
ELSEVIER SCIENCE INC2023pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration
Martin Vetterli, Paul Hurley, Eric Bezzam, Sepand Kashani, Matthieu Martin Jean-André Simeoni
Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...
2022Practical Multiple-Scattering Sheen Using Linearly Transformed Cosines
We introduce a new volumetric sheen BRDF that approximates scattering observed in surfaces covered with normally-oriented fibers. Our previous sheen model was motivated by measured cloth reflectance, but lacked significant backward scattering. The model pr ...
ASSOC COMPUTING MACHINERY2022On discrete Fourier uniqueness sets in Euclidean space
In this paper we present a new construction of a discrete Fourier uniqueness set in Euclidean space. ...
ICM2022Function Integration, Reconstruction And Approximation Using Rank-1 Lattices
Fabio Nobile, Giovanni Migliorati
We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...
2021Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations
Fabio Nobile, Simone Brugiapaglia
We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...
2020Fourier Sampling in Signal Processing and Numerical Linear Algebra
This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...
EPFL2020A Fourier-accelerated volume integral method for elastoplastic contact
Jean-François Molinari, Guillaume Anciaux, Lucas Henri Galilée Frérot
The contact of solids with rough surfaces plays a fundamental role in physical phenomena such as friction, wear, sealing, and thermal transfer. However, its simulation is a challenging problem due to surface asperities covering a wide range of length-scale ...
2019