Related papers: Fast computation of magnetostatic fields by Non-un…
Magnetic gears offer significant advantages over mechanical gears, including contactless power transfer, but require efficient and accurate modeling tools for optimization and commercialization. This paper presents the first fast and…
We prove classical simulation hardness, under the generalized $\mathsf{P}\neq\mathsf{NP}$ conjecture, for quantum circuit families with applications in near-term chemical ground state estimation. The proof exploits a connection to particle…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Neural network force field (NNFF) is a method for performing regression on atomic structure-force relationships, bypassing expensive quantum mechanics calculation which prevents the execution of long ab-initio quality molecular dynamics…
A linear-complexity algorithm for computing the Wasserstein-1 distance on non-uniform meshes is proposed. This work extends the fast Sinkhorn algorithms from [Q. Liao et al., Commun. Math. Sci., 20(2022)] and [Q. Liao et al., J. Sci.…
We prove well-posedness of time-dependent Ginzburg--Landau system in a nonconvex polygonal domain, and decompose the solution as a regular part plus a singular part. We see that the magnetic potential is not in $H^1$ in general, and the…
A general and fast method is conceived for computing the cyclic convolution of n points, where n is a prime number. This method fully exploits the internal structure of the cyclic matrix, and hence leads to significant reduction of the…
The Fast Multipole Method (FMM) is well known to possess a bottleneck arising from decreasing workload on higher levels of the FMM tree [Greengard and Gropp, Comp. Math. Appl., 20(7), 1990]. We show that this potential bottleneck can be…
Magnetic moments near zigzag edges in graphene allow complex nanostructures with customised spin properties to be realised. However, computational costs restrict theoretical investigations to small or perfectly periodic structures. Here we…
We present a new method for computing the Near-To-Far-Field (NTFF) transformation in FDTD simulations which has an overall scaling of $O(N^3)$ instead of the standard $O(N^4)$. By mapping the far field with a cartesian coordinate system the…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
This paper presents a novel methodology for fast simulation and analysis of transient heat transfer. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of…
The Fast Multipole Method (FMM) is an efficient numerical algorithm for computation of long-ranged forces in $N$-body problems within gravitational and electrostatic fields. This method utilizes multipole expansions of the Green's function…
Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
This paper presents experimental validation of the homogenized harmonic balance finite element method (HomHBFEM), which we have developed as a dedicated simulation technique for magnets with fast excitation cycles, in particular the fast…
We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…
We introduce a fast Fourier spectral method to compute linearized collision operators of the Boltzmann equation for variable hard-sphere gases. While the state-of-the-art method provides a computational cost O(MN^4 log N), with N being the…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are…