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Parallel Surrogate-Based Optimization (PSBO) is an efficient approach to deal with black-box time-consuming objective functions. According to the available computational budget to solve a given problem, three classes of algorithms are ...

This article presents a comprehensive study on the convergence behavior of the Dirichlet-Neumann Waveform Relaxation algorithm applied to solve the time fractional sub-diffusion and diffusion-wave equations in multiple subdomains, considering the ...

In this work, the two-stage multisplitting iteration methods based on the equivalent modulus equations are analyzed for solving linear complementarity problems. New convergence results are presented where the convergence domains of the parameter ...

• Propose two convergence theorems of the two-stage multisplitting iteration methods for LCPs with new proof techniques.
• The given results can improve the domain of the parameter matrices in the existing literatures.
• Design an ...

In this paper, we study the large N behavior of the smallest eigenvalue λ N of the ( N + 1 ) × ( N + 1 ) Hankel matrix, H N = ( μ j + k ) 0 ≤ j , k ≤ N, generated by the γ dependent Jacobi weight w ( z , γ ) = e − γ z z α ( 1 − z ) β , z ∈ [ 0 , ...

To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard–Lindelöf iteration), where at each iteration a linear inhomogeneous system of ...

In this paper, we describe an upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and scalability in the computation of the pressure field at each time step of the numerical procedure for ...

We propose a new parallel discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not require the ...

Discrete gradients (DG) or more exactly discrete gradient methods are time integration schemes that are custom-built to preserve first integrals or Lyapunov functions of a given ordinary differential equation (ODE). In conservative molecular ...

Matrices arising from the space–time boundary element method for the heat equation are dense and are global in space and time. Thus, they require a large amount of memory which may pose a problem when accelerating the code using GPUs. In this ...

• Space–time approach to time-dependent problems as opposed to time-stepping.
• Space–time boundary element method for the heat equation.
• Matrices not stored in memory, using a matrix-free method instead.
• GPUs to accelerate ...

A novel local and parallel multigrid method is proposed in this study for solving the semilinear Neumann problem with nonlinear boundary condition. Instead of solving the semilinear Neumann problem directly in the fine finite element space, we ...

This paper first presents a high-efficient and accurate coupled meshless algorithm for solving the multi-dimensional Gross–Pitaevskii equation (GPE) in unbounded domain, which is implemented on CUDA-program-based two-GPUs cards. The proposed novel ...

Due to an increased computational complexity of calculating the values of the distributed-order Caputo fractional derivative compared to the classical Caputo derivative there is a need to develop new techniques that accelerate it. In this paper ...$\mathrm{}$$\mathrm{}$

The paper presents a benchmark suite of ten non-serial polyadic dynamic programming (NPDP) kernels, which are designed to test the efficiency of tiled code generated by polyhedral optimization compilers. These kernels are mainly ...

• NPDP Benchmark Suite for the Evaluation of Automatic Optimizing Compilers.
• NPDP ...

In this work, we investigate a single projection method with double inertial extrapolation steps and self-adaptive step sizes for solving pseudomonotone variational inequality problems in a real Hilbert space. Weak and linear ...

• Deep insight on both sequential and parallel GMRES for linear systems.
• Rich discussion on the convergence and acceleration of GMRES.
• Brief account of other problems and block algorithms.

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We first consider basic algorithms and study their convergence. We then focus on acceleration strategies and parallel algorithms that are useful for solving ...

Elastoplasticity is observed in a wide range of materials like metals that have real-world applications. The design and optimization process of such materials depends strongly on elastoplastic analysis for the prediction of displacement and ...$$$$$$$$$$$$$$$$

Bandwidth reduction can be a first step in the computation of eigenvalues and eigenvectors for a wide-banded complex Hermitian (or real symmetric) matrix. We present algorithms for this reduction and the corresponding back-...

• Bandwidth reduction for eigensystem computation is considered.
• A two-level ...

Motivated and inspired by the works of Ceng et al. (2010) and Yao and Postolache (2012), we first study a relaxed inertial Tseng’s method for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous ...

Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion, “...

In this paper, we introduce a new class of hybrid inertial and contraction proximal point algorithm for the variational inclusion problem of the sum of two mappings in Hilbert spaces. We prove that the proposed algorithm converges strongly to a ...$\mathcal{}$