Natural zeolites in the Aksitero sedimentary formation of the western Luzon area of the Philippines were evaluated. The natural washed zeolite (NW-Z) was preconditioned with acid to purify it and increase its surface area. Acid treatment with 3 M HCl for 12 h yielded optimum acid treatment of the NW-Z, causing increases in the Si/Al ratio, the specific surface area by 32.5% and the porosity of the acid-treated zeolite (HC-Z). The HC-Z was washed with 4 M NaCl for 3, 6, 12, 18, 24, 48 and 72 h to improve its cation-exchange capacity for copper. The sodium-treated zeolite (Na-Z) was immersed in 100 ppm CuSO4 solution to test the copper-uptake capacity. Pretreatment of HC-Z with 4 M NaCl for 24 h is optimal for sodium treatment of the preconditioned HC-Z. The preconditioning techniques did not significantly alter the structure and morphology of the zeolite samples. It is suggested that the preconditioned Philippine natural zeolite samples are readily available for further functionalization that will enhance their antibacterial, catalytic and adsorption properties, with various useful applications in the field of catalysis, biomedicine, environmental mitigation and wastewater treatment.

This paper describes an adaptive preconditioner for numerical continuation of incompressible Navier–Stokes flows based on Stokes preconditioning [42] which has been used successfully in studies of pattern formation in convection. The preconditioner takes the form of the Helmholtz operator I–ΔtL which maps the identity (no preconditioner) for Δt≪1 to Laplacian preconditioning for Δt≫1. It is built on a first order Euler time-discretization scheme and is part of the family of matrix-free methods. The preconditioner is tested on two fluid configurations: three-dimensional doubly diffusive convection and a two-dimensional projection of a shear flow. In the former case, it is found that Stokes preconditioning is more efficient for , away from the values used in the literature. In the latter case, the simple use of the preconditioner is not sufficient and it is necessary to split the system of equations into two subsystems which are solved simultaneously using two different preconditioners, one of which is parameter dependent. Due to the nature of these applications and the flexibility of the approach described, this preconditioner is expected to help in a wide range of applications.

This experiment evaluated production and health parameters among cattle offered concentrates containing inorganic or organic complexed sources of supplemental Cu, Co, Mn and Zn during a 45-day preconditioning period. In total, 90 Angus×Hereford calves were weaned at 7 months (day −1), sorted by sex, weaning BW and age (261±2 kg; 224±2 days), and allocated to 18 drylot pens (one heifer and four steers per pen) on day 0; thus, all pens had equivalent initial BW and age. Pens were randomly assigned to receive a corn-based preconditioning concentrate containing: (1) Cu, Co, Mn and Zn sulfate sources (INR), (2) Cu, Mn, Co and Zn complexed organic source (AAC) or (3) no Cu, Co, Mn and Zn supplementation (CON). From day 0 to 45, cattle received concentrate treatments (2.7 kg/animal daily, as-fed basis) and had free-choice access to orchardgrass (Dactylis glomerata L.), long-stem hay and water. The INR and AAC treatments were formulated to provide the same daily amount of Co, Cu, Mn and Zn at a 50-, 16-, 8- and ninefold increase, respectively, compared with the CON treatment. On day 46, cattle were transported to a commercial feedlot, maintained as a single pen, and offered a free-choice receiving diet until day 103. Calf full BW was recorded on days −1 and 0, 45 and 46, and 102 and 103 for average daily gain (ADG) calculation. Liver biopsy was performed on days 0 (used as covariate), 22 and 45. Cattle were vaccinated against respiratory pathogens on days 15, 29 and 46. Blood samples were collected on days 15, 29, 45, 47, 49, 53 and 60. During preconditioning, mean liver concentrations of Co, Zn and Cu were greater (P⩽0.03) in AAC and INR compared with CON. No treatment effects were detected (P⩾0.17) for preconditioning feed intake, ADG or feed efficiency. No treatment effects were detected (P⩾0.48) for plasma concentrations of antibodies against Mannheimia haemolytica, bovine viral diarrhea types 1 and 2 viruses. Plasma haptoglobin concentrations were similar among treatments (P=0.98). Mean plasma cortisol concentration was greater (P⩽0.04) in CON compared with INR and AAC. No treatment effects were detected (P⩾0.37) for cattle ADG during feedlot receiving. Hence, INR and AAC increased liver concentrations of Co, Zn and Cu through preconditioning, but did not impact cattle performance and immunity responses during preconditioning and feedlot receiving.

We generalize the accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems. These methods involve four iteration parameters whose special choices can recover the preconditioned HSS and accelerated HSS iteration methods. Also a new efficient case is introduced and we theoretically prove that this new method converges to the unique solution of the saddle-point problem. Numerical experiments are used to further examine the effectiveness and robustness of iterations.

Based on the relaxed factorization techniques studied recently and the idea of the simple-like preconditioner, a modified relaxed positive-semidefinite and skew-Hermitian splitting (MRPSS) preconditioner is proposed for generalized saddle point problems. Some properties, including the eigenvalue distribution, the eigenvector distribution and the minimal polynomial of the preconditioned matrix are studied. Numerical examples arising from the mixed finite element discretization of the Oseen equation are illustrated to show the efficiency of the new preconditioner.

Preconditioned modified Hermitian and skew-Hermitian splitting method (PMHSS) is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equations, and uses one parameter α. Adding another parameter β, the generalized PMHSS method (GPMHSS) is essentially a twoparameter iteration method. In order to accelerate the GPMHSS method, using an unexpected way, we propose an accelerated GPMHSS method (AGPMHSS) for large complex symmetric linear systems. Numerical experiments show the numerical behavior of our new method.

A lopsided alternating direction iteration (LADI) method and an induced block diagonal preconditioner for solving block two-by-two generalised saddle point problems are presented. The convergence of the LADI method is analysed, and the block diagonal preconditioner can accelerate the convergence rates of Krylov subspace iteration methods such as GMRES. Our new preconditioned method only requires a solver for two linear equation sub-systems with symmetric and positive definite coefficient matrices. Numerical experiments show that the GMRES with the new preconditioner is quite effective.

A generalized preconditioned modified Hermitian and skew-Hermitian splitting (GPMHSS) real-valued iteration method is proposed for a class of complex symmetric indefinite linear systems. Convergence theory is established and the spectral properties of an associated preconditioned matrix are analyzed. We also give several variants of the GPMHSS preconditioner and consider the spectral properties of the preconditioned matrices. Numerical examples illustrate the effectiveness of our proposed method.

In this paper we consider PDE-constrained optimization problems which incorporate an H1 regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

About thirty years ago, Achi Brandt wrote a seminal paper providing a convergence theory for algebraic multigrid methods [Appl. Math. Comput., 19 (1986), pp. 23–56]. Since then, this theory has been improved and extended in a number of ways, and these results have been used in many works to analyze algebraic multigrid methods and guide their developments. This paper makes a concise exposition of the state of the art. Results for symmetric and nonsymmetric matrices are presented in a unified way, highlighting the influence of the smoothing scheme on the convergence estimates. Attention is also paid to sharp eigenvalue bounds for the case where one uses a single smoothing step, allowing straightforward application to deflation-based preconditioners and two-level domain decomposition methods. Some new results are introduced whenever needed to complete the picture, and the material is self-contained thanks to a collection of new proofs, often shorter than the original ones.

An entropy stable fully discrete shock capturing space-time Discontinuous Galerkin (DG) method was proposed in a recent paper to approximate hyperbolic systems of conservation laws. This numerical scheme involves the solution of a very large nonlinear system of algebraic equations, by a Newton-Krylov method, at every time step. In this paper, we design efficient preconditioners for the large, non-symmetric linear system, that needs to be solved at every Newton step. Two sets of preconditioners, one of the block Jacobi and another of the block Gauss-Seidel type are designed. Fourier analysis of the preconditioners reveals their robustness and a large number of numerical experiments are presented to illustrate the gain in efficiency that results from preconditioning. The resulting method is employed to compute approximate solutions of the compressible Euler equations, even for very high CFL numbers.

Preconditioning calf programs, while not new, are becoming more prevalent. They provide benefits to cow-calf producers while adding value for feeder cattle buyers. However, questions remain regarding the economic costs and returns of such programs. A model was estimated with data from three consecutive-day sales, to determine the value that buyers place on preconditioning programs and related feeder cattle traits. Our results indicate that price premiums, although evident, appear to be insufficient by themselves to cover the marginal costs of preconditioning.

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the success of using the classical projection method as a preconditioner for the coupled velocity pressure system [B. E. Griffith, J. Comp. Phys., 228 (2009), pp. 7565-7595], as well; established techniques for steady and unsteady Stokes flow in the finite-element literature, we construct preconditioners that employ independent generalized Helmholtz and Poisson solvers for the velocity and pressure subproblems. We demonstrate that only a single cycle of a standard geometric multigrid algorithm serves as an effective inexact solver for each of these subproblems. Contrary to traditional wisdom, we find that the Stokes problem can be solved nearly as efficiently as the independent pressure and velocity subproblems, making the overall cost of solving the Stokes system comparable to the cost of classical projection or fractional step methods for incompressible flow, even for steady flow and in the presence of large density and viscosity contrasts. Two of the five preconditioners considered here are found to be robust to GMRES restarts and to increasing problem size, making them suitable for large-scale problems. Our work opens many possibilities for constructing novel unsplit temporal integrators for finite-volume spatial discretizations of the equations of low Mach and incompressible flow dynamics.

This paper presents a method for solving the linear semi-implicit immersed boundary equations which avoids the severe time step restriction presented by explicit-time methods. The Lagrangian variables are eliminated via a Schur complement to form a purely Eulerian saddle point system, which is preconditioned by a projection operator and then solved by a Krylov subspace method. From the viewpoint of projection methods, we derive an ideal preconditioner for the saddle point problem and compare the efficiency of a number of simpler preconditioners that approximate this perfect one. For low Reynolds number and high stiffness, one particular projection preconditioner yields an efficiency improvement of the explicit IB method by a factor around thirty. Substantial speed-ups over explicit-time method are achieved for Reynolds number below 100. This speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.

Hypoxic-ischemic encephalopathy (HIE) caused by fetal and perinatal asphyxia is an important cause of mortality in the neonatal period. Not only will asphyxia affect the brain but also other organs such as the liver and kidneys. Interestingly, it has been shown that liver damage is proportional to the severity of the asphyctic insult, implying an association between liver impairment and HIE. Accordingly, we investigated in an established rat model the acute and chronic hepatic response to both fetal (FA) and perinatal asphyxia (PA). In addition, we assessed whether fetal asphyctic preconditioning (PC) would have any beneficial effect on the liver. Inflammation, ceramide signaling and hepatocellular damage were analyzed in the livers of newborn and adult rats at several short- and long-term time points after both FA and PA. We found that although FA induced an acute inflammatory response, apoptotic mRNA levels and oxidative DNA damage were decreased at 96 h post FA. Whereas increased IL-6 and IL-10 mRNA levels were observed after PA, the combination of FA and PA (PC) attenuated the inflammatory response. Moreover, 6 h after PA anti-apoptotic genes were downregulated and associated with less lipid peroxidation, while preconditioned animals were comparable to controls. In summary, asphyctic PC seems to have an acute protective effect on the liver by modulating the inflammatory, apoptotic and anti-oxidative response. More insight into the hepatic response to asphyxia is necessary, as disturbed hepatic function is associated with metabolic diseases in later life.

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

For solving linear complementarity problems LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting. But up to now, no paper has discussed the effect of preconditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and we use a class of preconditioners with generalized Accelerated Overrelaxation (GAOR) methods and analyze the convergence of these methods for LCP. Furthermore, Comparison between our methods and other non-preconditioned methods for the studied problem shows a remarkable agreement and reveals that our models are superior in point of view of convergence rate and computing efficiency. Besides, by choosing the appropriate parameters of these methods, we derive same results as the other iterative methods such as AOR, JOR, SOR etc. Finally the method is tested by some numerical experiments.

In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive-definite matrix with a complex shift. We study iterative methods for such systems, considering the basic and preconditioned versions of first the Richardson algorithm and then a conjugate gradient method.

Explicit time stepping schemes for the immersed boundary method require very small time steps in order to maintain stability. Solving the equations that arise from an implicit discretization is difficult. Recently, several different approaches have been proposed, but a complete understanding of this problem is still emerging. A multigrid method is developed and explored for solving the equations in an implicit-time discretization of a model of the immersed boundary equations. The model problem consists of a scalar Poisson equation with conformation-dependent singular forces on an immersed boundary. This model does not include the inertial terms or the incompressibility constraint. The method is more efficient than an explicit method, but the efficiency gain is limited. The multigrid method alone may not be an effective solver, but when used as a preconditioner for Krylov methods, the speed-up over the explicit-time method is substantial. For example, depending on the constitutive law for the boundary force, with a time step 100 times larger than the explicit method, the implicit method is about 15-100 times more efficient than the explicit method. A very attractive feature of this method is that the efficiency of the multigrid preconditioned Krylov solver is shown to be independent of the number of immersed boundary points.