Related papers: Fast computation of magnetostatic fields by Non-un…
We present new efficient (O(N log N)) methods for computing three quantities crucial to electronic structure calculations: the ionic potential, the electron-ion contribution to the Born-Oppenheimer forces, and the electron-ion contribution…
This paper developes a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points…
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
The full-wave simulation of complex electromagnetic surfaces such as reflectarrays and metasurfaces is a challenging problem. In this paper, we present a macromodeling approach to efficiently simulate complex electromagnetic surfaces…
Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…
Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem for over 40 years. An early result by Morgenstern from 1973, provides an $\Omega(n…
Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
Convolution models with long filters have demonstrated state-of-the-art reasoning abilities in many long-sequence tasks but lag behind the most optimized Transformers in wall-clock time. A major bottleneck is the Fast Fourier Transform…
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…
The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient…
A new approach for the parallel forward modeling of transient electromagnetic (TEM) fields is presented. It is based on a family of uniform-in-time rational approximants to the matrix exponential that share a common denominator independent…
We use lookup tables to design faster algorithms for important algebraic problems over finite fields. These faster algorithms, which only use arithmetic operations and lookup table operations, may help to explain the difficulty of…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…
The current Bayesian FFT algorithm relies on direct differentiation to obtain the posterior covariance matrix (PCM), which is time-consuming, memory-intensive, and hard to code, especially for the multi-setup operational modal analysis…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the $N$th coefficient of an algebraic series uses differential equations and has…
Long sequence neural memory remains a challenging problem. RNNs and their variants suffer from vanishing gradients, and Transformers suffer from quadratic scaling. Furthermore, compressing long sequences into a finite fixed representation…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate…