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The singular vectors of a chemical transport model are the directions of maximum perturbation growth over a finite time interval. They have proved useful for the estimation of error growth, the initialization of ensemble forecasts, and the optimal placement of adaptive observations. The aim of this paper is to address computational aspects of singular vector analysis for atmospheric chemical transport models. The distinguishing feature of these models is the presence of stiff chemical interactions. A projection approach to preserve the symmetry of the tangent linear–adjoint operator for stiff systems is discussed, and extended to 3D chemical transport simulations. Numerical results are presented for a simulation of atmospheric pollution in East Asia in March 2001. The singular values and the structure of the singular vectors depend on the length of the simulation interval, the meteorological data, the location of the optimization region and the selection of optimization species, the choice of error norms, and the size of the optimization region.

SUMMARYA fourth-order compact finite-difference method is proposed in this paper to solve the system of two-dimensional Burgers' equations. The new method is based on the two-dimensional Hopf-Cole transformation, which transforms the system of two-dimensional Burgers' equations into a linear heat equation. The linear heat equation is then solved by an implicit fourth-order compact finite-difference scheme. A compact fourth-order formula is also developed to approximate the boundary conditions of the heat equation, while the initial condition for the heat equation is approximated using Simpson's rule to maintain the overall fourth-order accuracy. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of this method.

An efficient higher-order finite difference algorithm is presented in this article for solving systems of twodimensional reaction-diffusion equations with nonlinear reaction terms. The method is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular five-point difference stencil similar to that used in the standard second-order algorithm, such as the Crank-Nicolson algorithm. The Padé approximation and Richardson extrapolation are used to achieve high-order accuracy in the spatial and temporal dimensions, respectively. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

In this article, we discuss a scheme for dealing with Neumann and mixed boundary conditions using a compact stencil. The resulting compact algorithm for solving systems of nonlinear reaction-diffusion equations is fourth-order accurate in both the temporal and spatial dimensions. We also prove that the standard second-order approximation to zero Neumann boundary conditions provides fourth-order accuracy when the nonlinear reaction term is independent of the spatial variables. Numerical examples, including an application of this algorithm to a mathematical model describing frontal polymerization process, are presented in the article to demonstrate the accuracy and efficiency of the scheme.

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BackgroundTo compare perioperative and oncological outcomes of pancreatic duct adenocarcinoma (PDAC) after laparoscopic versus open pancreaticoduodenectomy (LPD vs. OPD), we performed a meta-analysis of currently available propensity score matching studies and large-scale retrospective cohorts to compare the safety and overall effect of LPD to OPD for patients with PDAC.MethodsA meta-analysis was registered at PROSPERO and the registration number is CRD42021250395. PubMed, Web of Science, EMBASE, Cochrane Central Register of Controlled Trials, and ClinicalTrials.gov databases were searched based on a defined search strategy to identify eligible studies before March 2021. Data on operative times, blood loss, 30-day mortality, reoperation, length of hospital stay (LOS), overall morbidity, Clavien–Dindo ≥3 complications, postoperative pancreatic fistula (POPF), blood transfusion, delayed gastric emptying (DGE), postpancreatectomy hemorrhage (PPH), and oncologic outcomes (R0 resection, lymph node dissection, overall survival, and long-term survival) were subjected to meta-analysis.ResultsOverall, we identified 10 retrospective studies enrolling a total of 11,535 patients (1,514 and 10,021 patients underwent LPD and OPD, respectively). The present meta-analysis showed that there were no significant differences in overall survival time, 1-year survival, 2-year survival, 30-day mortality, Clavien-Dindo ≥3 complications, POPF, DGE, PPH, and lymph node dissection between the LPD and OPD groups. Nevertheless, compared with the OPD group, LPD resulted in significantly higher rate of R0 resection (OR: 1.22; 95% CI 1.06–1.40; p = 0.005), longer operative time (WMD: 60.01 min; 95% CI 23.23–96.79; p = 0.001), lower Clavien–Dindo grade ≥III rate (p = 0.02), less blood loss (WMD: −96.49 ml; 95% CI −165.14 to −27.83; p = 0.006), lower overall morbidity rate (OR: 0.65; 95% CI 0.50 to 0.85; p = 0.002), shorter LOS (MD = −2.73; 95% CI −4.44 to −1.03; p = 0.002), higher 4-year survival time (p = 0.04), 5-year survival time (p = 0.001), and earlier time to starting adjuvant chemotherapy after surgery (OR: −10.86; 95% CI −19.42 to −2.30; p = 0.01).ConclusionsLPD is a safe and feasible alternative to OPD for patients with PDAC, and compared with OPD, LPD seemed to provide a similar OS.Systematic Review Registrationhttps://www.crd.york.ac.uk/PROSPERO/#recordDetails.

Full-waveform inversion (FWI) has emerged as a powerful strategy for estimating subsurface model parameters by iteratively minimizing the difference between synthetic data and observed data. The Hessian-free (HF) optimization method represents an attractive alternative to Newton-type and gradient-based optimization methods. At each iteration, the HF approach obtains the search direction by approximately solving the Newton linear system using a matrix-free conjugate-gradient (CG) algorithm. The main drawback with HF optimization is that the CG algorithm requires many iterations. In our research, we develop and compare different preconditioning schemes for the CG algorithm to accelerate the HF Gauss-Newton (GN) method. Traditionally, preconditioners are designed as diagonal Hessian approximations. We additionally use a new pseudo diagonal GN Hessian as a preconditioner, making use of the reciprocal property of Green’s function. Furthermore, we have developed an [Formula: see text]-BFGS inverse Hessian preconditioning strategy with the diagonal Hessian approximations as an initial guess. Several numerical examples are carried out. We determine that the quasi-Newton [Formula: see text]-BFGS preconditioning scheme with the pseudo diagonal GN Hessian as the initial guess is most effective in speeding up the HF GN FWI. We examine the sensitivity of this preconditioning strategy to random noise with numerical examples. Finally, in the case of multiparameter acoustic FWI, we find that the [Formula: see text]-BFGS preconditioned HF GN method can reconstruct velocity and density models better and more efficiently compared with the nonpreconditioned method.