Least-squares reverse time migration (LSRTM) is an advanced seismic imaging technique that reconstructs subsurface models by minimizing the residuals between simulated and observed data. Mathematically, the LSRTM inversion of the sub-surface reflecti...
A reduced-dimension robust Capon beamforming method using Krylov subspace techniques (RDRCB) is a diagonal loading algorithm with low complexity, fast convergence and strong anti-interference ability. The diagonal loading level of RDRCB is known to b...
The study of heat transfer deals with the determination of the rate of heat energy transfer from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often the fundamental principle behind severa...
A flexible extended Krylov subspace method (
The stochastic finite element method is an important tool for structural reliability analysis. In order to improve the calculation efficiency, a stochastic finite element method based on the Krylov subspace is proposed for the static reliability anal...
To better simulate the prices of underlying assets and improve the accuracy of pricing financial derivatives, an increasing number of new models are being proposed. Among them, the Lévy process with jumps has received increasing attention beca...
This paper describes a Krylov subspace iterative method designed for solving linear systems of equations with a large, symmetric, nonsingular, and indefinite matrix. This method is tailored to enable the evaluation of error estimates for the computed...
When a straight cylindrical conductor of finite length is electrostatically charged, its electrostatic potential
After nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the optimi...
This paper presents an analysis of the time complexity of algorithms prepared for solving heat transfer problems at nanoscale. The first algorithm uses the classic Dual-Phase-Lag model, whereas the second algorithm employs a reduced version of the mo...
An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based...
In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term
Implicit integration factor (IIF) methods were developed for solving time-dependent stiff partial differential equations (PDEs) in literature. In [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368–388], IIF methods are designed to eff...
In order to overcome the computational challenges associated with block preconditioners for Krylov subspace methods, particularly those arising from Schur complement systems, this paper proposes an improved new block (INB) preconditioner for solving...
Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF)...
Tempered fractional diffusion equations constitute a critical class of partial differential equations with broad applications across multiple physical domains. In this paper, the Crank–Nicolson method and the tempered weighted and shifted Gr&uu...
We derive a double-optimal iterative algorithm (DOIA) in an m-degree matrix pencil Krylov subspace to solve a rectangular linear matrix equation. Expressing the iterative solution in a matrix pencil and using two optimization techniques, we determine...
This article reviews the linear solvers available in OpenFOAM and assesses their impact on the convergence behaviour of the SIMPLE algorithm. The discretisation of transport equations in CFD results in large and sparse linear systems, for which the c...
In this paper, we propose a semi-implicit difference scheme for solving one-dimensional nonlinear space-fractional diffusion equations. The method is first-order accurate in time and second-order accurate in space. It uses a fractional central differ...
Total fractional-order variation (TFOV) in image deblurring problems can reduce/remove the staircase problems observed with the image deblurring technique by using the standard total variation (TV) model. However, the discretization of the Euler–Lagr...
The most popular iterative methods for solving nonsymmetric linear systems are Krylov methods. Recently, an optimal Quasi-ORthogonal (Q-OR) method was introduced, which yields the same residual norms as the Generalized Minimum Residual (GMRES) method...
In this work, we propose a nonlinear dynamic inverse solution to the diffusion problem based on Krylov Subspace Methods with spatiotemporal constraints. The proposed approach is applied by considering, as a forward problem, a 1D diffusion problem wit...
Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed...
The PageRank model computes the stationary distribution of a Markov random walk on the linking structure of a network, and it uses the values within to represent the importance or centrality of each node. This model is first proposed by Google for ra...
The adaptive cubic regularization method solves an unconstrained optimization model by using a three-order regularization term to approximate the objective function at each iteration. Similar to the trust-region method, the calculation of the sub-pro...
In this paper, we propose a fast linear power flow method using a constant impedance load model to simulate both the entire Low Voltage (LV) and Medium Voltage (MV) networks in a single simulation. Accuracy and efficiency of this linear approach are...
In this paper, we consider the numerical solution of a large complex linear system with a saddle-point form obtained by the discretization of the time-harmonic eddy-current optimal control problem. A new Schur complement is proposed for this algebrai...
As a model that possesses both the potentialities of Caputo time fractional diffusion equation (Caputo-TFDE) and symmetric two-sided space fractional diffusion equation (Riesz-SFDE), time-space fractional diffusion equation (TSFDE) is widely applied...
The study of matrix functions is highly significant and has important applications in control theory, quantum mechanics, signal processing, and machine learning. Previous work has mainly focused on how to use the Krylov-type method to efficiently cal...
Multibody dynamics (MBD) simulations involving hundreds to thousands of bodies give rise to large-scale, sparse, and structurally indefinite linear systems. Traditional direct solvers incur prohibitive memory and computational costs, while iterative...
Exponential integrator (EI) method based on Krylov subspace approximation is a promising method for large-scale transient circuit simulation. However, it suffers from the singularity problem and consumes large subspace dimensions for stiff circuits w...
GMRES is one of the most powerful and popular methods to solve linear systems in the Krylov subspace; we examine it from two viewpoints: to maximize the decreasing length of the residual vector, and to maintain the orthogonality of the consecutive re...
As semiconductor technologies continue to scale aggressively, electromigration (EM) has become critical in modern VLSI design. Since traditional EM assessment methods fail to accurately capture the complex behavior of multi-segment interconnects, rec...
Fractional derivatives and regime-switching models are widely used in various fields of finance because they can describe the nonlocal properties of the solutions and the changes in the market status, respectively. The regime-switching time-fractiona...
In the transient analysis of an engineering power electronics device, the order of its equivalent circuit model is excessive large. To eliminate this issue, some model order reduction (MOR) methods are proposed in the literature. Compared to other MO...
A double optimal solution (DOS) of a least-squares problem
Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-s...
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode Decomposition-type methods in t...
The traditional three-dimensional (3D) magnetotelluric (MT) forward modeling using Krylov subspace algorithms has the problem of low modeling efficiency. To improve the computational efficiency of 3D MT forward modeling, we present a novel geometric...
In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper. We pro...
Microelectromechanical Systems (MEMS) is difficult to take transient analysis due to the tight coupling between the multiple energy domains, typically nonlinear. An effective increment-dimensional precise integration method (PIM) combined with the mo...
In this paper, we propose a new numerical method based on the extended block Arnoldi algorithm for solving large-scale differential nonsymmetric Stein matrix equations with low-rank right-hand sides. This algorithm is based on projecting the initial...
The purpose of this work is to study the efficient numerical solvers for time-dependent conservative space fractional diffusion equations. Specifically, for the discretized Toeplitz-like linear system, we aim to study efficient preconditioning based...
In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their correspondi...
In this work, we proposed a dynamic inverse solution with spatio-temporal constraints of the nonlinear heat diffusion problem in 1D and 2D based on a regularized Gauss–Newton and Krylov subspace with a preconditioner. The preconditioner is comp...
The increasing complexity of modern Very Large-Scale Integration (VLSI) circuits, combined with unavoidable variations in physical and manufacturing parameters, poses significant challenges for accurate and efficient circuit simulation. Parametric mo...
In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coup...
The repeated updating of parametric designs is computationally challenging, especially for large-scale multi-physics models. This work is focused on proposing an efficient modal modification method for gradient-based topology optimization of thermoel...
GPU cards have been used for scientific calculations for many years. Despite their ever-increasing performance, there are cases where they may still have problems. This article addresses possible performance and memory issues and their solutions that...
For solving the continuous Sylvester equation, a class of Hermitian and skew-Hermitian based multiplicative splitting iteration methods is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous...
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