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Jasper A Vrugt - One of the best experts on this subject based on the ideXlab platform.

  • Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and Matlab Implementation
    Environmental Modelling and Software, 2016
    Co-Authors: Jasper A Vrugt
    Abstract:

    Bayesian inference has found widespread application and use in science and engineering to reconcile Earth system models with data, including prediction in space (interpolation), prediction in time (forecasting), assimilation of observations and deterministic/stochastic model output, and inference of the model parameters. Bayes theorem states that the posterior probability, p(H|Y~) of a hypothesis, H is proportional to the product of the prior probability, p( H) of this hypothesis and the likelihood, L(H|Y~) of the same hypothesis given the new observations, Y~, or p(H|Y~)∝p(H)L(H|Y~). In science and engineering, H often constitutes some numerical model, ℱ(x) which summarizes, in algebraic and differential equations, state variables and fluxes, all knowledge of the system of interest, and the unknown parameter values, x are subject to inference using the data Y~. Unfortunately, for complex system models the posterior distribution is often high dimensional and analytically intractable, and sampling methods are required to approximate the target. In this paper I review the basic theory of Markov chain Monte Carlo (MCMC) simulation and introduce a Matlab toolbox of the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm developed by Vrugt et al. (2008a, 2009a) and used for Bayesian inference in fields ranging from physics, chemistry and engineering, to ecology, hydrology, and geophysics. This Matlab toolbox provides scientists and engineers with an arsenal of options and utilities to solve posterior sampling problems involving (among others) bimodality, high-dimensionality, summary statistics, bounded parameter spaces, dynamic simulation models, formal/informal likelihood functions (GLUE), diagnostic model evaluation, data assimilation, Bayesian model averaging, distributed computation, and informative/noninformative prior distributions. The DREAM toolbox supports parallel computing and includes tools for convergence analysis of the sampled chain trajectories and post-processing of the results. Seven different case studies illustrate the main capabilities and functionalities of the Matlab toolbox.

  • Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and Matlab Implementation
    eScholarship University of California, 2016
    Co-Authors: Jasper A Vrugt
    Abstract:

    © 2015 Elsevier Ltd. Bayesian inference has found widespread application and use in science and engineering to reconcile Earth system models with data, including prediction in space (interpolation), prediction in time (forecasting), assimilation of observations and deterministic/stochastic model output, and inference of the model parameters. Bayes theorem states that the posterior probability, p(H|Y~) of a hypothesis, H is proportional to the product of the prior probability, p( H) of this hypothesis and the likelihood, L(H|Y~) of the same hypothesis given the new observations, Y~, or p(H|Y~)∝p(H)L(H|Y~). In science and engineering, H often constitutes some numerical model, ℱ(x) which summarizes, in algebraic and differential equations, state variables and fluxes, all knowledge of the system of interest, and the unknown parameter values, x are subject to inference using the data Y~. Unfortunately, for complex system models the posterior distribution is often high dimensional and analytically intractable, and sampling methods are required to approximate the target. In this paper I review the basic theory of Markov chain Monte Carlo (MCMC) simulation and introduce a Matlab toolbox of the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm developed by Vrugt et al. (2008a, 2009a) and used for Bayesian inference in fields ranging from physics, chemistry and engineering, to ecology, hydrology, and geophysics. This Matlab toolbox provides scientists and engineers with an arsenal of options and utilities to solve posterior sampling problems involving (among others) bimodality, high-dimensionality, summary statistics, bounded parameter spaces, dynamic simulation models, formal/informal likelihood functions (GLUE), diagnostic model evaluation, data assimilation, Bayesian model averaging, distributed computation, and informative/noninformative prior distributions. The DREAM toolbox supports parallel computing and includes tools for convergence analysis of the sampled chain trajectories and post-processing of the results. Seven different case studies illustrate the main capabilities and functionalities of the Matlab toolbox

O. Sigmund - One of the best experts on this subject based on the ideXlab platform.

  • A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D
    Structural and Multidisciplinary Optimization, 2020
    Co-Authors: Federico Ferrari, O. Sigmund
    Abstract:

    Compact and efficient Matlab Implementations of compliance topology optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125 lines respectively. On discretizations ranging from 3 ⋅ 10^4 to 4.8 ⋅ 10^5 elements, the 2D version, named top99neo , shows speedups from 2.55 to 5.5 times compared to the well-known top88 code of Andreassen et al. (Struct Multidiscip Optim 43(1):1–16, 2011 ). The 3D version, named top3D125 , is the most compact and efficient Matlab Implementation for 3D TO to date, showing a speedup of 1.9 times compared to the code of Amir et al. (Struct Multidiscip Optim 49(5):815–829, 2014 ), on a discretization with 2.2 ⋅ 10^5 elements. For both codes, improvements are due to much more efficient procedures for the assembly and Implementation of filters and shortcuts in the design update step. The use of an acceleration strategy, yielding major cuts in the overall computational time, is also discussed, stressing its easy integration within the basic codes.

  • A 99 line topology optimization code written in Matlab
    Structural and Multidisciplinary Optimization, 2001
    Co-Authors: O. Sigmund
    Abstract:

    The paper presents a compact Matlab Implementation of a topology optimization code for compliance minimization of statically loaded structures. The total number of Matlab input lines is 99 including optimizer and Finite Element subroutine. The 99 lines are divided into 36 lines for the main program, 12 lines for the Optimality Criteria based optimizer, 16 lines for a mesh-independency filter and 35 lines for the finite element code. In fact, excluding comment lines and lines associated with output and finite element analysis, it is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem. By adding three additional lines, the program can solve problems with multiple load cases. The code is intended for educational purposes. The complete Matlab code is given in the Appendix and can be down-loaded from the web-site http://www.topopt.dtu.dk.

Aapo Nummenmaa - One of the best experts on this subject based on the ideXlab platform.

  • a software toolkit for tms electric field modeling with boundary element fast multipole method an efficient Matlab Implementation
    Journal of Neural Engineering, 2020
    Co-Authors: Sergey N Makarov, William A Wartman, Mohammad Daneshzand, Kyoko Fujimoto, Tommi Raij, Aapo Nummenmaa
    Abstract:

    Objective To present and disseminate our transcranial magnetic stimulation (TMS) modeling software toolkit, including several new algorithmic developments, and to apply this software to realistic TMS modeling scenarios given a high-resolution model of the human head including cortical geometry and an accurate coil model. Approach The recently developed charge-based boundary element fast multipole method (BEM-FMM) is employed as an alternative to the 1st order finite element method (FEM) most commonly used today. The BEM-FMM approach provides high accuracy and unconstrained numerical field resolution close to and across cortical interfaces. Here, the previously proposed BEM-FMM algorithm has been improved in several novel ways. Main results The improvements resulted in a threefold increase in computational speed while maintaining the same solution accuracy. The computational code based on the Matlab® platform is made available to all interested researchers, along with a coil model repository and examples to create custom coils, head model repository, and supporting documentation. The presented software toolkit may be useful for post-hoc analyses of navigated TMS data using high-resolution subject-specific head models as well as accurate and fast modeling for the purposes of TMS coil/hardware development. Significance TMS is currently the only non-invasive neurostimulation modality that enables painless and safe supra-threshold stimulation by employing electromagnetic induction to efficiently penetrate the skull. Accurate, fast, and high resolution modeling of the electric fields may significantly improve individualized targeting and dosing of TMS and therefore enhance the efficiency of existing clinical protocols as well as help establish new application domains.

  • a software toolkit for tms electric field modeling with boundary element fast multipole method an efficient Matlab Implementation
    bioRxiv, 2020
    Co-Authors: Sergey N Makarov, William A Wartman, Mohammad Daneshzand, Kyoko Fujimoto, Tommi Raij, Aapo Nummenmaa
    Abstract:

    Abstract Background Transcranial magnetic stimulation (TMS) is currently the only non-invasive neurostimulation modality that enables painless and safe supra-threshold stimulation by employing electromagnetic induction to efficiently penetrate the skull. Accurate, fast, and high resolution modeling of the electric fields (E-fields) may significantly improve individualized targeting and dosing of TMS and therefore enhance the efficiency of existing clinical protocols as well as help establish new application domains. Objective To present and disseminate our TMS modeling software toolkit, including several new algorithmic developments, and to apply this software to realistic TMS modeling scenarios given a high-resolution model of the human head including cortical geometry and an accurate coil model. Method The recently developed charge-based boundary element fast multipole method (BEM-FMM) is employed as an alternative to the 1st order finite element method (FEM) most commonly used today. The BEM-FMM approach provides high accuracy and unconstrained field resolution close to and across cortical interfaces. Here, the previously proposed BEM-FMM algorithm has been improved in several novel ways. Results and Conclusions The improvements resulted in a threefold increase in computational speed while maintaining the same solution accuracy. The computational code based on the Matlab® platform is made available to all interested researchers, along with a coil model repository and examples to create custom coils, head model repository, and supporting documentation. The presented software toolkit may be useful for post-hoc analyses of navigated TMS data using high-resolution subject-specific head models as well as accurate and fast modeling for the purposes of TMS coil/hardware development.

Ivan F. M. Menezes - One of the best experts on this subject based on the ideXlab platform.

  • PolyTop: a Matlab Implementation of a general topology optimization framework using unstructured polygonal finite element meshes
    Structural and Multidisciplinary Optimization, 2012
    Co-Authors: Cameron Talischi, Glaucio H. Paulino, Anderson Pereira, Ivan F. M. Menezes
    Abstract:

    We present an efficient Matlab code for structural topology optimization that includes a general finite element routine based on isoparametric polygonal elements which can be viewed as the extension of linear triangles and bilinear quads. The code also features a modular structure in which the analysis routine and the optimization algorithm are separated from the specific choice of topology optimization formulation. Within this framework, the finite element and sensitivity analysis routines contain no information related to the formulation and thus can be extended, developed and modified independently. We address issues pertaining to the use of unstructured meshes and arbitrary design domains in topology optimization that have received little attention in the literature. Also, as part of our examination of the topology optimization problem, we review the various steps taken in casting the optimal shape problem as a sizing optimization problem. This endeavor allows us to isolate the finite element and geometric analysis parameters and how they are related to the design variables of the discrete optimization problem. The Matlab code is explained in detail and numerical examples are presented to illustrate the capabilities of the code.

Valdman Jan - One of the best experts on this subject based on the ideXlab platform.

  • Minimization of p-Laplacian via the Finite Element Method in Matlab
    2021
    Co-Authors: Matonoha Ctirad, Moskovka Alexej, Valdman Jan
    Abstract:

    Minimization of energy functionals is based on a discretization by the finite element method and optimization by the trust-region method. A key tool is a local evaluation of the approximated gradients together with sparsity of the resulting Hessian matrix. We describe a vectorized Matlab Implementation of the p-Laplace problem in one and two space-dimensions, however it is easily applicable to other energy formulations.Comment: 8 pages, 3 figure, submitted proceeding of conference LSSC 2021, Sozopo

  • Matlab Implementation of Element-based Solvers
    2020
    Co-Authors: Marcinkowski Leszek, Valdman Jan
    Abstract:

    Rahman and Valdman (2013) introduced a vectorized way to assemble finite element stiffness and mass matrices in Matlab. Local element matrices are computed all at once by array operations and stored in multi-dimentional arrays (matrices). We build some iterative solvers on available multi-dimentional structures completely avoiding the use of a sparse matrix.Comment: 8 pages, 3 figures, conference LSSC 2019, Sozopol, Bulgaria, to appear as Springer LNCS 1195

  • Efficient and flexible Matlab Implementation of 2D and 3D elastoplastic problems
    'Elsevier BV', 2019
    Co-Authors: Čermák Martin, Sysala Stanislav, Valdman Jan
    Abstract:

    Fully vectorized Matlab Implementation of various elastoplastic problems formulated in terms of displacement is considered. It is based on implicit time discretization, the finite element method and the semismooth Newton method. Each Newton iteration represents a linear system of equations with a tangent stiffness matrix. We propose a decomposition of this matrix consisting of three large sparse matrices representing the elastic stiffness operator, the strain-displacement operator, and the derivative of the stress-strain operator. The first two matrices are fixed and assembled once and only the third matrix needs to be updated in each iteration. Assembly times of the tangent stiffness matrices are linearly proportional to the number of plastic integration points in practical computations and never exceed the assembly time of the elastic stiffness matrix. Matlab codes are available for download and provide complete finite element Implementations in both 2D and 3D assuming von Mises and Drucker-Prager yield criteria. One can also choose several finite elements and numerical quadrature rules.Web of Science35561459

  • Efficient and flexible Matlab Implementation of 2D and 3D elastoplastic problems
    2018
    Co-Authors: Čermák Martin, Sysala Stanislav, Valdman Jan
    Abstract:

    We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in Matlab using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with hardening and several yield criteria. The problems are formulated in terms of displacements, discretized by the implicit Euler method in time and the finite element method in space, and solved by the semismooth Newton method. We discuss in detail selected models with the von Mises and Prager-Drucker yield criteria and four types of finite elements. The related codes are available for download. A particular interest is devoted to the assembling of tangential stiffness matrices. Since these matrices are repeatedly constructed in each Newton iteration and in each time step, we propose another vectorized assembling than current ones known for the elastic stiffness matrices. The main idea is based on a construction of two large and sparse matrices representing the strain-displacement and tangent operators, respectively, where the former matrix remains fixed and the latter one is updated only at some integration points. Comparisons with other available Matlab codes show that our technique is also efficient for purely elastic problems. In elastoplasticity, the assembly times are linearly proportional to the number of integration points in a plastic phase and additional times due to plasticity never exceed assembly time of the elastic stiffness matrix.Comment: 21 pages, 10 figure