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First-principles density functional theory (DFT) with plane wave (PW) basis set is the most widely used method in quantum mechanical material simulations due to its advantages in accuracy and universality. However, a perceived drawback of…
The linear combination of atomic orbitals (LCAO) method uses a small basis set in exchange for expensive matrix element calculations. The most efficient approximation for the matrix element calculations is the two-center approximation (2CA)…
Molecule-metal interfaces have a broad range of applications in nanoscale materials science. Accurate characterization of their electronic structures from first-principles is key in understanding material and device properties. The GW…
The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented…
Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted density matrix renormalization group method that acts on a…
The physics of electronic energy level alignment at interfaces formed between molecules and metals can in general be accurately captured by the \emph{ab initio} $GW$ approach. However, the computational cost of such $GW$ calculations for…
For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we…
The shortest paths problem is a fundamental challenge in graph theory, with a broad range of potential applications. The algorithms based on matrix multiplication exhibits excellent parallelism and scalability, but is constrained by high…
A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating…
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, {\em without restricting to variational ansatzes}. The lattice of size $N$ is partitioned into two subclusters. At…
Accurate and fast calculations of localized surface plasmon resonances (LSPR) in metallic nanoparticles is essential for applications in sensing, nano-optics, and energy harvesting. Although full-wave numerical techniques such as the…
Extended formulation of Full Waveform Inversion (FWI), called Wavefield Reconstruction Inversion (WRI), offers potential benefits of decreasing the nonlinearity of the inverse problem by replacing the explicit inverse of the ill-conditioned…
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…
A thick-restart Lanczos type algorithm is proposed for Hermitian $J$-symmetric matrices. Since Hermitian $J$-symmetric matrices possess doubly degenerate spectra or doubly multiple eigenvalues with a simple relation between the degenerate…
We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be…
The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…
The increasing deployment of massive active antenna arrays in low Earth orbit (LEO) satellites necessitates computationally efficient and adaptive precoding techniques to mitigate dynamic channel variations and enhance spectral efficiency.…
Elastic metasurfaces offer precise control over elastic waves for applications such as vibration isolation, sensing, and imaging. However, achieving high-efficiency and scattering-free performance with complex functionalities remains a…
In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of…
Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in…