Showing papers in "Journal of Computational Physics in 2015"
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TL;DR: Results for a SNAP potential for tantalum are presented, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases.
643 citations
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TL;DR: A new difference analog of the Caputo fractional derivative (called the L 2 - 1 σ formula) is constructed and some difference schemes generating approximations of the second and fourth order in space and the second order in time for the time fractional diffusion equation with variable coefficients are considered.
546 citations
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TL;DR: Two criteria for required by a fractional operator are formulated and the Grunwald-Letnikov, Riemann-Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria.
351 citations
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TL;DR: This paper proposes and analyzes an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions using shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives.
277 citations
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TL;DR: The initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain is considered and nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived.
235 citations
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TL;DR: A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
218 citations
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TL;DR: The coherence-optimal sampling scheme is proposed: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support.
217 citations
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TL;DR: The results reveal that the method is very effective and simple in determination of solution of the fractional KdV-Burgers equation.
208 citations
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TL;DR: A novel combination of methods for the numerical approximation of solutions to the Serre-Green-Naghdi equations preserves the robustness of the original finite-volume Saint-Venant solver, in particular for the treatment of wetting/drying and equilibrium states.
200 citations
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TL;DR: A novel approach to build such a surrogate model from a design of experiments using the selected polynomials as regression functions for the universal Kriging model, which seems to be an optimal solution between the two other classical approaches.
199 citations
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TL;DR: An energy conservative Crank–Nicolson difference scheme for nonlinear Riesz space-fractional Schrodinger equations is studied and the existence of the difference solution is proved based on Brouwer fixed point theorem.
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TL;DR: An efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense.
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TL;DR: It is shown that for a given computational budget, basis selection produces a more accurate PCE than would be obtained if the basis were fixed a priori.
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TL;DR: The scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable, and it is proved that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme.
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TL;DR: An exponentially accurate fractional spectral collocation method for solving linear/nonlinear FPDEs with field-variable order and a spectral penalty method for enforcing inhomogeneous initial conditions are developed.
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TL;DR: The results demonstrate that variable-order fractional derivatives can be used to model the physics of anomalous transport with spatiotemporal variability but also as new effective numerical tools that can deal with the long-standing issues of outflow boundary conditions and monotonicity of integer-order PDEs.
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TL;DR: Numerical results show the reliability of the proposed solver for multiphase flows with high density ratio and high Reynolds number, and has the capability and advantage to simulate multiphases flows on non-uniform grids.
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TL;DR: An improved SPH model for multiphase flows with complex interfaces and large density differences is developed, and a corrected density re-initialization is applied to improve computational accuracy and to obtain smooth pressure fields.
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TL;DR: The proposed collocation scheme, both in temporal and spatial discretizations, is successfully extended to solve the two-dimensional TFSE, demonstrating the utility and high accuracy of the new approach over other numerical methods.
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TL;DR: The proposed quasi-compact difference scheme is proved to be unconditionally stable and convergent in L2 norm for both 1D and 2D cases.
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TL;DR: An improved 3D bubble dynamics model based on Boundary Element Method demonstrates good accuracy and stability, and more toroidal bubble evolution detailed features are captured which are in accordance with the axisymmetric model.
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TL;DR: Why and how the discontinuous Galerkin (DG) formulation can be used for under-resolved turbulence simulations without explicit subgrid-scale modelling is clarified and the use of higher polynomial orders along with moderately coarser meshes is shown to be the best way to translate available degrees of freedom into resolution power.
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TL;DR: A novel methodology based on active subspaces is employed to characterize the effects of the input uncertainty on the scramjet performance, and this dimension reduction enables otherwise infeasible uncertainty quantification.
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TL;DR: The work required for executing this data-to-prediction process-measured in number of forward (and adjoint) ice sheet model solves-is independent of the state dimension, parameter dimension, data dimension, and the number of processor cores.
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TL;DR: A new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function.
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TL;DR: In this paper, a class of two-dimensional space and time fractional Bloch-Torrey equations (2D-STFBTEs) are considered and a semi-discrete variational formulation for 2D- STFB TEs is obtained by finite difference method and Galerkin finite element method.
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TL;DR: The parametrization conditions enable the MRT LBE to provide viscosity-independent truncation spatial errors and are supported with the high-order accurate boundary conditions confirmed in touching arrays of spheres.
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TL;DR: The capability of MDEIM to generate accurate and efficient ROMs is demonstrated on the solution of two computationally-intensive classes of problems occurring in engineering contexts, namely PDE-constrained shape optimization and parametrized coupled problems.
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TL;DR: Numerical simulations of the approximate solution of the time-fractional variable order telegraph equation were presented for different values of the grid point.
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TL;DR: An error estimator is derived which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error, independent of physical parameters, such as the contrast and multiple scales in the problem.