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AbstractA new algorithm for convection-dominated diffusion equations is proposed. Based on the domain decomposition method (DDM), the algorithm integrates the Samarskii scheme and the Jacobi explicit scheme with explicit/implicit coupling to provide parallelism. The domain decomposition method decomposes a large global problem into multiple sub-problems which can be solved on multiple processors in parallel. The parallel algorithm without needing numerical correction can obtain accuracy of Samarskii scheme while maintaining unconditional stability, which marks a step forward compared to the previous DDM. Both theoretical analysis and numerical examples show the accuracy and efficiency of the new algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the conservation characteristic difference method based on the second-order modified upwind scheme is analyzed for solving the two-dimensional convection-diffusion equations by combining the splitting technique. Along each directional, the intermediate numerical solutions are first computed by the piecewise parabolic method (PPM), where the endpoint values over each domain are solved by the second-order modified upwind scheme. Then, the solutions are computed by the splitting implicit characteristic difference method. By some auxiliary lemmas, we can prove that our scheme is stable in L 2 -norm. The optimal error estimate is given and the scheme is convergent of second order in space. Numerical experiments are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

The split common fixed point problem is an optimization challenge that involves finding an element within one fixed point set such that when transformed by a bounded linear operator, it belongs to another fixed point set. This problem falls under the category of inverse problems in mathematics. We present a novel self-adaptive algorithm based on double inertial steps for solving the split common fixed point problem for demicontractive mappings. We also establish a weak convergence theorem for our method. Furthermore, we also present some numerical experiments illustrating the convergence behavior and the efficiency of our proposed algorithm. [ABSTRACT FROM AUTHOR]

We present a matrix-free parallel scalable multilevel deflation preconditioned method for heterogeneous time-harmonic wave problems. Building on the higher-order deflation preconditioning proposed by Dwarka and Vuik (SIAM J. Sci. Comput. 42(2):A901-A928, 2020; J. Comput. Phys. 469:111327, 2022) for highly indefinite time-harmonic waves, we adapt these techniques for parallel implementation in the context of solving large-scale heterogeneous problems with minimal pollution error. Our proposed method integrates the Complex Shifted Laplacian preconditioner with deflation approaches. We employ higher-order deflation vectors and re-discretization schemes derived from the Galerkin coarsening approach for a matrix-free parallel implementation. We suggest a robust and efficient configuration of the matrix-free multilevel deflation method, which yields a close to wavenumber-independent convergence and good time efficiency. Numerical experiments demonstrate the effectiveness of our approach for increasingly complex model problems. The matrix-free implementation of the preconditioned Krylov subspace methods reduces memory consumption, and the parallel framework exhibits satisfactory parallel performance and weak parallel scalability. This work represents a significant step towards developing efficient, scalable, and parallel multilevel deflation preconditioning methods for large-scale real-world applications in wave propagation. [ABSTRACT FROM AUTHOR]

In this work, for solving large sparse vertical linear complementarity problems, a relaxation two-step modulus-based synchronous multisplitting method without auxiliary variable is constructed. The convergence conditions are presented for the proposed method, where the range of the relaxation parameters is obtained. By OpenACC framework, the proposed method is shown to be more efficient than the existing method with high speedups with numerical tests. [ABSTRACT FROM AUTHOR]

We develop a fully asynchronous proximal bundle method for solving non-smooth, convex optimization problems. The algorithm can be used as a drop-in replacement for classic bundle methods, i.e., the function must be given by a first-order oracle for computing function values and subgradients. The algorithm allows for an arbitrary number of master problem processes computing new candidate points and oracle processes evaluating functions at those candidate points. These processes share information by communication with a single supervisor process that resembles the main loop of a classic bundle method. All processes run in parallel and no explicit synchronization step is required. Instead, the asynchronous and possibly outdated results of the oracle computations can be seen as an inexact function oracle. Hence, we show the convergence of our method under weak assumptions very similar to inexact and incremental bundle methods. In particular, we show how the algorithm learns important structural properties of the functions to control the inaccuracy induced by the asynchronicity automatically such that overall convergence can be guaranteed. [ABSTRACT FROM AUTHOR]

This paper provides an overview of the new features of the finite element library deal.II, version 9.6. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel approach to approximate the solution of variational inequality problems without relying on the monotonicity assumption. We propose a two-step inertial modified projection and contraction method for solving quasi-monotone and without-monotone variational inequalities in real Hilbert spaces. We establish a weak convergence result for the proposed method under suitable conditions. Additionally, numerical examples and a network equilibrium flow problem are provided to illustrate the effectiveness of our method and compare it with recent related methods in the literature. [ABSTRACT FROM AUTHOR]

The primary focus of this study is how to expedite the convergence rate of the extragradient method by tactfully choosing inertial parameters and building up the step-size rule. To achieve this goal, we introduce three improvements to Korpelevich's extragradient method. These improvements include the use of dual inertial steps as well as a self-adaptive step-size rule. The proposed iterative techniques are employed for solving equilibrium problems in real Hilbert spaces. Initially, we establish the results for weak convergence of the proposed methods, assuming the involved bifunction to be both pseudomonotone and Lipschitz-type continuous. Subsequently, we demonstrate linear convergence in scenarios where the bifunction is strongly pseudomonotone and Lipschitz-type continuous. Finally, we present multiple numerical experiments to illustrate the practical effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Trends over the past two decades indicate that much of the performance gains of commercial optimization solvers is due to improvements in x86 hardware. To continue making progress, it is critical to consider alternative/specialized massively parallel computing architectures. In this work, we detail the development of an open-source source code transformation approach built using Symbolics.jl to construct McCormick-based relaxations of functions that enables their effective parallelized evaluation. We then apply this approach in a novel parallelized branch-and-bound routine that offloads lower- and upper-bounding problems to a GPU. The effectiveness of this new approach is demonstrated on three nonconvex problems of interest, where it yields convergence time improvements of 22–118x compared to an equivalent serial CPU implementation and in two cases outperforms vanilla branch-and-bound versions of existing state-of-the-art solvers that use tighter bounding techniques. This work exemplifies how deterministic global optimizers using alternative hardware architectures can compete with—or eventually outclass—even the most powerful serial CPU implementations, and to the best of the authors' knowledge, represents the first successful demonstration of deterministic global optimization using a GPU. [ABSTRACT FROM AUTHOR]

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods. [ABSTRACT FROM AUTHOR]

At present, a large number of fractional differential models of migration processes in soils are developed. Their practical application largely depends on the possibility to determine the values of their parameters. In this regard, we study the possibility of recovering the values of parameters for one such generalized model from noised data in order to assess the threshold of measurement accuracy, beyond which the complication of a model leads to an inability to distinguish its solutions from the solutions of simpler models. We consider the 1D fractional-order model of water head dissipation in water-saturated soil with linear deformation that includes the Caputo–Fabrizio derivative with respect to the time variable and the Riemann–Liouville derivative with respect to the space variable. Direct problems for this model are proposed to be solved by an optimized computational procedure based on a finite-difference scheme. Inverse problems of model's parameter identification are solved using a multi-threaded Particle Swarm Optimization technique. The results of computational experiments showed that the values of model parameters can be restored with less than 10 % relative error for the number of input water head values equal to 1000 and the level of noise less than 5 % . Our results also show that the order of the Riemann–Liouville derivative can be with an average relative error of less than 3 % restored even at 10 % level of noise and 40 input values, when the accuracy of other parameters' restoration drops significantly. [ABSTRACT FROM AUTHOR]

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 presence of some heterogeneous media. Our analysis focuses on estimating the convergence rate of the algorithm and investigates how this estimate varies with different fractional orders. Furthermore, we extend our analysis to encompass the 2D sub-diffusion case. To validate our findings, we conduct numerical experiments to verify the estimated convergence rate. The results confirm the theoretical estimates and provide empirical evidence for the algorithm’s efficiency and reliability. Moreover, we push the boundaries of the algorithm’s applicability by extending it to solve the time fractional Allen-Chan equation, a problem that exceeds our initial theoretical estimates. Remarkably, we observe that the algorithm performs exceptionally well in this extended scenario for both short and long-time windows. [ABSTRACT FROM AUTHOR]

In this article we mainly propose a numerical scheme, based on the novel Stochastic Grid Bundling Method (SGBM), to price American options in the presence of counterparty credit risk. More precisely, we consider the regression techniques (regress later) employed in the SGBM method and take advantage of the bundling structure to develop an efficient parallel strategy that is implemented on a GPU architecture. Also, a novel interpolation-based technique is efficiently applied in the XVA computation. Besides the advantages obtained in the sequential version, when compared with the more classical Least Squares Method, we show the relevant speedup of the parallel GPU-based version with respect to the sequential CPU-based one. [ABSTRACT FROM AUTHOR]

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 solving a Large Eddy Simulation formulation of the incompressible Navier–Stokes equations. We developed a software module in the Alya's kernel to interface the libraries included in the current version of PSCToolkit, a framework for the iterative solution of sparse linear systems, on parallel distributed-memory computers, by Krylov methods coupled to Algebraic MultiGrid preconditioners. The Toolkit has undergone various extensions within the EoCoE-II project with the primary goal of facing the exascale challenge. Results on a realistic benchmark for airflow simulations in wind farm applications show that the PSCToolkit solvers significantly outperform the original versions of the Conjugate Gradient method available in the Alya's kernel in terms of scalability and parallel efficiency and represent a very promising software layer to move the Alya code toward exascale. [ABSTRACT FROM AUTHOR]

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 dynamics (MD) simulations, the energy of the system is constant and therefore a first integral of motion. Hence, discrete gradient methods seem to be a natural choice as an integration scheme in conservative molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

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 differential equations has to be solved. This is done by the exponential block Krylov subspace (EBK) method. Thus, we have an inner-outer iterative method, where iterative approximations are determined over a certain time interval, with no time stepping involved. This approach has recently been shown to be efficient as a time-parallel integrator within the PARAEXP framework. In this paper, convergence behavior of this method is assessed theoretically and practically. We examine efficiency of the method by testing it on nonlinear Burgers, Liouville–Bratu–Gelfand, and nonlinear heat conduction equations and comparing its performance with that of conventional time-stepping integrators. [ABSTRACT FROM AUTHOR]

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 transform it into a linear boundary value problem defined in each level of a multigrid sequence and a small-scale semilinear Neumann problem defined in a low-dimensional correction subspace. Furthermore, the linear boundary value problem can be efficiently solved using local and parallel methods. The proposed process derives an optimal error estimate with linear computational complexity. Additionally, compared with existing multigrid methods for semilinear Neumann problems that require bounded second order derivatives of nonlinear terms, ours only needs bounded first order derivatives. A rigorous theoretical analysis is proposed in this paper, which differs from the maturely developed theories for equations with Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

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 assembly and resolution of large linear systems for the time iterations. The approach is based on a kinetic representation of the system of conservation laws previously investigated by the authors. Coulette et al. (in: Springer proceedings in mathematics & statistics, Springer, Berlin, pp 171–178, 2017. ), Badwaik et al. (ESAIM Proc Surv; 63:60–77, 2018. ), Coulette et al. (Comput Fluids; 190:485–502, 2019. ), Drui et al. (CR Mécanique; 347(3):259–269, 2019. ) and Gerhard et al. (Comput Math Appl; 112:116–137, 2022. . ). In this paper, the approach is extended with a subdomain strategy that improves the parallel scaling of the method on computers with distributed memory. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new modified algorithm for finding an element of the set of solutions of a pseudomonotone, Lipschitz continuous variational inequality problem in real Hilbert spaces. Using the technique of double inertial steps into a single projection method we give weak and strong convergence theorems of the proposed algorithm. The weak convergence does not require prior knowledge of the Lipschitz constant of the variational inequality mapping and only computes one projection onto a feasible set per iteration as well as without using the sequentially weak continuity of the associated mapping. Under additional strong pseudomonotonicity and Lipschitz continuity assumptions, the R-linear convergence rate of the proposed algorithm is presented. Finally, some numerical examples are given to illustrate the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a relaxed two-step modulus-based matrix synchronous multisplitting iteration method for solving the linear complementarity problems is constructed. The convergence conditions of the proposed method are analyzed with the convergence range of the relaxation parameters. Some parallel numerical experiments under OpenACC framework are given to show that the proposed method can accelerate the convergence rate of the existing method significantly. [ABSTRACT FROM AUTHOR]

The numerical solution of the Helmholtz equations is challenging to compute when the wave numbers contained in the governing equation are large. In this paper, we present a parallel algorithm for this problem. A class of sixth-order hybrid compact finite-difference schemes for the Helmholtz equations is presented based on the Taylor expansion. To improve the efficiency of solving the large-wave-number problem, we implemented a parallel algorithm based on the Message Passing Interface environment to solve the discrete system. The validity and accuracy of the proposed method are verified by numerical examples. The method is also applicable to solving problems with oscillatory solutions, which are characterized by numerical instability as the wave number increases. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a non-overlapping substructuring type algorithm for the Cahn–Hilliard equation. Being a nonlinear equation, it is of great importance to develop a robust numerical method for investigating the solution behaviour of the CH equation. We present the formulation of the Neumann–Neumann method applied to the CH equation and study its convergence behaviour in one and two spatial dimension for two subdomains and also extend the method for logarithmic nonlinearity. We also present the nonlinear NN method for the CH equation. We illustrate the theoretical results by providing numerical examples. [ABSTRACT FROM AUTHOR]

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 high-performance scheme (RDFPM-PML-GPU) is mainly motived by the items below: (a) a reduced-dimensional finite pointset method (RDFPM) is first presented to solve the 2D/3D spatial derivatives in GPE, which has lower calculated amount than the traditional FPM (TFPM) for the derivatives; (b) the perfectly matched layer (PML) technique is adopted to treat the absorbing boundary conditions (ABCs) which is used for the infinite exterior region, and the time-splitting technique is resorted to reduce the computing complexity in PML; (c) a fast parallel algorithm based on CUDA-program is proposed to accelerate the computation in the proposed meshless scheme with local matrix on two GPUs. The numerical convergent rate and advantages of the proposed meshless scheme are demonstrated by solving two examples, which include the comparisons between the proposed RDFPM and TFPM, the merit of easily implemented local refinement point distribution in meshless method, and the merit of PML-ABCs over the zero Dirichlet boundary treatment for unbounded domain. Meanwhile, the high efficiency of the proposed GPU-based parallelization algorithm is tested and discussed by simulating 3D examples, which shows that the speed-up rate is about 500-times of using two-GPUs over a single CPU. Finally, the proposed RDFPM-PML-GPU method is used to predict the long-time evolution of quantum vortex in 2D/3D GPEs describing Bose–Einstein condensates. All the numerical tests show the high-performance and flexible application of the proposed parallel meshless algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose and present a non-overlapping substructuring-type iterative algorithm for the Cahn–Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet–Neumann (DN) methods applied to the CH equation and study the convergence behaviour in one and two spatial dimensions in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method. [ABSTRACT FROM AUTHOR]

The numerical simulation of the flow in oil reservoirs has become, over decades, a standard tool applied by the oil and gas industry to forecast the behavior of a hydrocarbon producing field. To reduce the computational effort of these simulations, which in general demand more time as the case studied becomes more realistic, like other researchers, we use high-performance computing techniques in reservoir simulation. In this context, the main contribution of this work is the proposal of a strategy for the numerical simulation of non-isothermal flow in oil reservoirs using an operator splitting, the OpenMP, a coprocessor, and a one-equation model for temperature without the need to consider local thermal equilibrium. Throughout the development of this work, we used a non-isothermal flow modeling in porous media, the control-volume finite-difference method for discretization, and a linearization of the non-linear algebraic equations by Picard’s method. Our main objective was the parallelization of the numerical code using the OpenMP and, from the variation in the number of threads used in the simulations, we were able to reach speedups higher than 45 in some cases. [ABSTRACT FROM AUTHOR]

The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.

We present a numerical method specifically designed for simulatingthree-dimensional fluid--structure interaction (FSI) problems based on thereference map technique (RMT). The RMT is a fully Eulerian FSI numerical methodthat allows fluids and large-deformation elastic solids to be represented on asingle fixed computational grid. This eliminates the need for meshing complexgeometries typical in other FSI approaches, and greatly simplifies the couplingbetween fluid and solids. We develop the first three-dimensional implementationof the RMT, parallelized using the distributed memory paradigm, to simulateincompressible FSI with neo-Hookean solids. As part of our new method, wedevelop a new field extrapolation scheme that works efficiently in parallel.Through representative examples, we demonstrate the method's accuracy andconvergence, as well as its suitability in investigating many-body and activesystems. The examples include settling of a mixture of heavy and buoyant softellipsoids, lid-driven cavity flow containing a soft sphere, and swimmersactuated via active stress.

Background: Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations, capable of accurately replicating both normal and pathological conditions, are still in the process of achieving full maturity within the scientific community. Results: This work introduces life x -ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both normal and pathological conditions. life x -ep employs the monodomain equation to model the heart's electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, life x -ep integrates the generation of myocardial fibers based on Laplace–Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within life x -fiber. As an alternative, users can also choose to import myofibers from a file. This paper provides a concise overview of the mathematical models and numerical methods underlying life x -ep, along with comprehensive implementation details and instructions for users. life x -ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of life x -ep through various idealized and realistic simulations conducted in both normal and pathological scenarios. Furthermore, the software offers a user-friendly and flexible interface, simplifying the setup of simulations using self-documenting parameter files. Conclusions: life x -ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface. life x -ep represents a valuable tool for conducting in silico patient-specific simulations. [ABSTRACT FROM AUTHOR]

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 for this purpose we propose to use a fast matrix "multiply and accumulate" operation available in GPU's that contain the so-called tensor cores. We present and experimentally analyze the properties of GPU-algorithms that are based on the L1 finite-difference approximation of the derivative and incorporate them into the Crank-Nicholson scheme for the distributed-order time-fractional diffusion equation. The computation of derivative's values on GPU was faster than the multi-threaded implementation on CPU only for a large number of time steps with growing performance gain when number of time steps increase. The usage of the single-precision data type increased the error up to 2.7 % comparing with the usage of the double-precision data type. Half-precision computations in tensor cores increased the error up to 29.5 % . While solving a time-fractional diffusion equation, algorithms implemented for GPU with the usage of the single-precision data type were at least three times faster than the CPU-implementation for the number of time steps more than 1280. Data type precision had only slight influence on the solution error with significantly increased execution time when the double-precision data type was used for data storage and processing. [ABSTRACT FROM AUTHOR]

Multilevel extensions of overlapping Schwarz domain decomposition preconditioners of Generalized Dryja–Smith–Widlund (GDSW) type are considered in this paper. The original GDSW preconditioner is a two-level overlapping Schwarz domain decomposition preconditioner, which can be constructed algebraically from the fully assembled stiffness matrix. The FROSch software, which belongs to the ShyLU package of the Trilinos software library, provides parallel implementations of different variants of GDSW preconditioners. The coarse problem can limit the parallel scalability of two-level GDSW preconditioners. As a remedy, in the past, three-level GDSW approaches have been proposed, which can significantly extend the range of scalability. Here, a multilevel extension of the GDSW preconditioner is introduced and analyzed. Finally, parallel results for the implementation in FROSch for up to 40 000 cores of the SuperMUC-NG supercomputer at Leibniz Supercomputing Centre (LRZ) and to 48 000 cores of the JUWELS supercomputer at Jülich Supercomputing Centre (JSC) are presented. [ABSTRACT FROM AUTHOR]

A geometric intrinsic pre-processing algorithm(GPA for short) for solving large-scale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun (in 2022–2023). Different from traditional preconditioning, the authors apply the intrinsic geometric invariance, the Grid matrix G and the discrete PDE mass matrix B, stiff matrix A satisfies commutative operator BG = GB and AG = GA, where G satisfies Gm = I, m ≪ dim(G). A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain. In this paper, the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle, square, tetrahedron, cube, and so on. They give the general form of pre-processing matrix, theory and numerical test of GPA. The conclusion that "the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron" is obtained through research, and it is further found that "commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm". [ABSTRACT FROM AUTHOR]

This paper provides an overview of the new features of the finite element library deal.II, version 9.5. [ABSTRACT FROM AUTHOR]

We come up with a new type of forward–backward–forward algorithms for monotone inclusion problems based on a self-adaptive technique to avoid the selection of Lipschitz assumption and also double inertial extrapolations to increase the convergence performance of our presented algorithm. We also prove its weak convergence theorem under mild hypothesis. Additionally, we provide numerical test in image deblurring and signal recovery as applications. The results show that our algorithm outperforms some known algorithms in the literature. [ABSTRACT FROM AUTHOR]