Static analysis of two-dimensional elastic structures using global collocation

Static and dynamic physically non-linear analysis of concrete structures using a hybrid mixed finite element model

A new hybrid-mixed stress model for the analysis of concrete structures using damage mechanics

Many modern global optimization algorithms are inspired by natural phenomena rather than classes of mathematical functions. Theorems such as No Free Lunch imply that an algorithm's performance on an objective function is determined by the compatibility between the function and its structure. Grouping by inspiration blurs the distinction between algorithms, making it harder to study compatibility. Therefore, this work treats algorithms as sequential sampling algorithms, and groups them by sampling scheme: 1. perturb every design (e.g., Particle Swarm), 2. perturb a subset of designs (e.g., rand/1/bin Differential Evolution), 3. perturb a single design (e.g., best/2/bin Differential Evolution), 4. deterministically modify and then perturb the design (e.g., Quantum Particle Swarm). Using 295 analytical test cases, the structure and performance of 38 biologically inspired algorithms (major and minor variations of 5 algorithms) are compared by group. The groups are evaluated by 1. how performance scales with dimensionality, and 2. trends in mean convergence rates and accuracy. Controlling for sample size, number of algorithms/group, convergence criteria, and tuning parameters, Groups 2 and 3 demonstrate superior accuracy and convergence rates on 80 % of test cases combined, implying greater overall compatibility than other groups, and scale much better than other groups on 2nd and 4th order polynomials up to 100-dimensions, converging to minima 3---6 orders of magnitude lower. Statistical significance testing reveals overlap in the behavior of certain Group 2 and 3 algorithms on 52 test cases. Group 3 is a special case of Group 2, further implying structural compatibility with certain test cases.

The objective of this study was to formulate a process to quantify the uncertainty associated with computational fluid dynamics (CFD) analysis. A generic, cone-nosed missile simulation using COBALT as the flow solver package was selected as a test case. The flow conditions were indicative of a missile traveling at Mach 3 at 30,000 feet above sea level. An unstructured meshing scheme was employed, using manual refinement and clustering to capture the flow characteristics. Three subsequent meshes were generated by doubling the spacing in every direction within the grid, creating four different mesh densities, with a constant, one-dimensional refinement ratio of 2. Two Grid Convergence Indices (GCl's) were then formulated, using the three finest meshes and the three coarsest meshes. The axial force value was the quantity of interest used to conduct the GCI analysis. The results of the first prediction, conducted with the three finest meshes, indicated that the exact solution fell within the range [590.527, 594.795], whereas the second study indicated that the exact value fell within the range [584.892, 612.992]. The exact solution is defined by the GCI study to be the Richardson Extrapolated value for a particular set of solutions. In other words, the exact value would be the predicted solution for a grid with grid spacing equal to zero. This process was then repeated on a simplified case over a blunt-body with a structured meshing scheme. The same flow conditions were used for this case as for the cone- nosed missile. The same trend was observed in the GCI results of the simplified case, showing that the GCI exact value range deduced from the denser meshes fell within the range of exact values produced from the coarser meshes. The results also indicated that the COBALT solver tended to produce second-order convergence values (p values) with respect to grid refinement. The values obtained for p in the missile tests were 2.03157 and 1.14883 for the fine and coarse GCI studies, respectively. In the blunt-body cases, the p values were found to be 1.95777 and 2.28039 for the fine and coarse meshes, respectively. It seemed odd at first that two of the resulting p values were greater than two, considering the fact that it is more usual for nominally second order solvers to produce p values slightly less than two. This can possible be attributed to the fact that the study was conducted assuming inviscid flow, and therefore the solver was only manipulating the convective terms from the Navier-Stokes equation while neglecting the diffusion terms. Many flow solvers will use higher order techniques to solve the convective terms, while using nominally second order techniques to solve the diffusion terms. Though this conclusion may not give any quantifiable measurement of the overall uncertainty associated with results of the aforementioned studies, the GCI study performed does provide a good indication of the uncertainty due to mesh resolution associated with the COBALT flow solver.

In this paper, we present the numerical results of the Boundary-Domain Integro-Differential Equation (BDIDE) associated to Dirichlet problem for an elliptic type Partial Differential Equation (PDE) with a variable coefficient. The numerical constructions are based on discretizing the boundary of the problem region by utilizing continuous linear iso-parametric elements while the domain of the problem region is meshed by using iso-parametric quadrilateral bilinear domain elements. We also use a semi-analytic method to handle the integration that exhibits logarithmic singularity instead of using Gauss-Laguare quadrature formula. The numerical results that employed the semi-analytic method give better accuracy as compared to those when we use Gauss-Laguerre quadrature formula. The system of equations that obtained by the discretized BDIDE is solved by an iterative method (Neumann series expansion) as well as a direct method (LU decomposition method). From our numerical experiments on all test domains, the relative errors of the solutions when applying semi-analytic method are smaller than when we use Gauss-Laguerre quadrature formula for the integration with logarithmic singularity. Unlike Dirichlet Boundary Integral Equation (BIE), the spectral properties of the Dirichlet BDIDE is not known. The Neumann iterations will converge to the solution if and only if the spectral radius of matrix operator is less than 1. In our numerical experiment on all the test domains, the Neumann series does converge. It gives some conclusions for the spectral properties of the Dirichlet BDIDE even though more experiments on the general Dirichlet problems need to be carried out.

Thermoelastic analysis by means of three-dimensional polyhedral elements based on the Smoothed Finite elements method (S-FEM), for example nodal Cell-based S-FEM (CS-FEM), Node-based S-FEM (NS-FEM), and Edge-based S-FEM (ES-FEM), was studied. S-FEM allows implicit shape functions, making it possible to construct shape functions of S-FEM based polyhedral elements in a straightforward manner. The performance of S-FEM based polyhedral elements was compared with one another and with the conventional finite elements including hexahedral and tetrahedral element. Numerical examples show that the polyhedral elements by means of CS-FEM and ES-FEM provide better accuracy and convergence rate than conventional hexahedral finite elements, while the polyhedral elements by means of NS-FEM leads to spurious mode.

Non-convergence often occurs in the solution of highly nonlinear problem by conventional implicit finite element method. As another choice, explicit method is sometimes used by researchers. Through 2 typical static and dynamic examples this paper verifies that explicit finite element method can provide the same exactness of calculation as the implicit method even in the situation that the duration of action exceeds the natural period of structure greatly. At the same time, compared with implicit method, explicit method possesses higher speed, more robust algorithm, and stronger nonlinear capability, so that explicit method can be applied in static and dynamic analysis of structures, especially in large deformation and highly nonlinear problem.

New expansions of numerical eigenvalues by finite elements

We investigate the convergence of quasiparticle energies for periodic systems to the thermodynamic limit using increasingly large simulation cells corresponding to increasingly dense integration meshes in reciprocal space. The quasiparticle energies are computed at the level of equation-of-motion coupled-cluster theory for ionization (IP-EOM-CC) and electron attachment processes (EA-EOM-CC). By introducing an electronic correlation structure factor, the expected asymptotic convergence rates for systems with different dimensionality are formally derived. We rigorously test these derivations through numerical simulations for trans-polyacetylene using IP/EA-EOM-CCSD and the G0W0@HF approximation, which confirm the predicted convergence behavior. Our findings provide a solid foundation for efficient schemes to correct finite-size errors in IP/EA-EOM-CCSD calculations.

This paper reports on the SIMPLE-like solution algorithm that significantly improves velocity–pressure coupling, leading to the accelerated convergence. The algorithm is applicable to both incompressible and compressible flows. It is implemented within the framework of a cell centered finite volume method using colocated storage of flow variables on unstructured grids. The convergence acceleration is an outcome of the novel treatment of the pressure correction equation that accounts for two commonly neglected terms appearing in a general pressure correction equation. These terms, namely, the neighbor and nonorthogonal corrections, represent velocity corrections from neighboring cells and the cell-face pressure correction gradient associated with the grid nonorthogonality, respectively. Reminiscent of the PISO method, both neighbor and nonorthogonal corrections are taken into account by performing two or more correction steps. However, the full inclusion of neighbor velocity corrections can prevent the solution convergence. Following an analogy between time marching and a steady-state iterative approach, this problem has been resolved by introducing a pseudounsteady term into discretized velocity correction equations. Using this term, the contribution of neighbor corrections is underrelaxed, enabling a satisfactory convergence rate. The algorithm is applied to several benchmark test cases, covering laminar and turbulent, as well as incompressible and compressible, flows. For all test cases, the convergence rate can be significantly improved by performing two or more pressure correction steps. An optimal number of pressure corrections exists for which a meaningful reduction of computing time is possible.

Hydrogen-based technologies are gaining traction as viable alternatives to fossil fuels, with polymer electrolyte membrane fuel cells (PEMFCs) playing a central role in clean energy systems. Accurate parameter identification remains essential for predictive modeling and control of PEMFCs. This study introduces an innovative application of the recently developed Puma Optimizer (PO) for the estimation of unknown parameters in a PEMFC dynamic model. PO's search dynamics are evaluated against five recent metaheuristic algorithms and a set of established optimization methods from the literature. The assessment relies on experimental voltage-current data obtained from two commercial PEMFC stacks, the 250 W and the NedStack PS6 units. Performance comparison is conducted using the sum of squared errors, standard deviation, convergence rate, and robustness metrics evaluated across multiple trials. Results demonstrate that PO achieves high accuracy in parameter estimation, fast convergence, and stable performance under varied initial conditions. PO consistently outperforms or matches the benchmark algorithms in all test cases. The findings confirm the potential of the puma optimizer as a reliable and efficient tool for modeling PEMFC systems, supporting improved system design, control, and optimization.

Accelerate the convergence of turbulent flows simulation: A novel progressive locally power-law preconditioning method

Benchmarking Active Subspace methods of global sensitivity analysis against variance-based Sobol' and Morris methods with established test functions

Extending FEniCS to work in higher dimensions using tensor product finite elements

This work presents a new type of non-conventional finite elements (FE) that utilize trigonometric-based shape functions. The selection of the shape functions is inspired by the analytical expression of structural modeshapes. The proposed element consists of two “regular” nodes and a middle “hidden” node that basically enriches the local approximation and leads to the partition-of-unity property. Two different element types are constructed: a rod element with axial degrees of freedom and a Timoshenko beam element with two degrees of freedom: vertical displacement and rotation. Both the proposed elements are tested against conventional 3-node FE in free vibration and transient dynamic simulations of isotropic rod and beam structures. Numerical results show that the proposed trigonometric FE yield more accurate estimations of natural frequencies than the traditional 3-node FE. Also, the maximum natural frequency of each case is not only more accurate but also has smaller numerical value. This leads to the selection of larger time steps when employing explicit time integration, resulting in lower computing times. Finally, the presented elements evince higher convergence rates than the conventional 3-node FE in wave propagation simulations of rods and beams, further increasing the proposed method’s efficiency. This is explicitly quantified, since the proposed FE appears to be twice as fast as the conventional 3-node FE, in obtaining a transient wave response with the same level of accuracy.