Analytic solver platform crack
The standard approach usually employs the solution of a previous time step as an initial guess, which might be too conservative. The iterative solver is used for solving the system of equations and requires a proper initial guess that has significant effect on the convergence. In this work, we additionally implement 3-D transient electromagnetic forward modeling using the backward Euler implicit scheme. We developed time-domain finite-difference modeling based on the explicit scheme earlier. This study compares the efficiency of 3-D transient electromagnetic forward modeling schemes on the multi-resolution grid for various modeling scenarios. The method was efficiently used for optimizing the default phase settings in the in-house-built 8Tx/16Rx arrays designed for cMRI in pigs at 7T. This strategy allows for (i) drastic reduction of the computation time in comparison to a brute-force method and (ii) finding phase vectors providing a combined B1+-field with homogeneity characteristics superior to the one provided by the random-multi-start optimization approach. The key point of the described method is the pre-selection of starting vectors for the iterative solver-based search to maximize the probability of finding a global extremum for a cost function optimizing the homogeneity of a shaped B1+-field. In this work, we propose a robust technique to find phase vectors providing optimization of the B1-homogeneity in the default setup of multiple-element transceiver arrays. This task is often solved by time-consuming (brute-force) or by limited efficiency optimization methods. One of the key steps in the design and fine-tuning of such arrays during the development process is finding the default driving phases for individual coil elements providing the best possible homogeneity of the combined B1+-field that is achievable without (or before) subject-specific B1+-adjustment in the scanner. The development of novel multiple-element transmit-receive arrays is an essential factor for improving B1+ field homogeneity in cardiac MRI at ultra-high magnetic field strength (B0 > = 7.0T). Numerical results show a noticeable increase in structure stiffness using the level parameter directly in the optimization problem than the state-of-art mapping technique. The reliability of the proposed approach has been validated with different engineering design cases. Based on the parameterized micro-structure, the optimization problem is solved concurrently with an iterative solver.
An additional constraint on the level parameter is introduced in the structural optimization framework to enhance adjacent cellulars interfaces’ compatibility. The stiffness matrices of the cellular structures derived as a function of the level parameters, using the homogenization results. A numerical homogenization method is employed to calculate the elasticity tensor of the cellular materials.
By introducing parameterized periodic cellular structures, the minimal surface level-parameter is defined as the material design parameter and is implemented directly in the optimization problem.
In this paper, instead of finding optimal properties of two scales separately, we reformulate the two-scale TO problem and optimize the design variables concurrently in both scales. The design domain is first discretized to a coarse scale, and the material property distribution is optimized, then using micro-structures to fill each property field. To address this issue, two-scale TO paves an avenue for high-resolution structural design. However, the increasingly finer design brings computational challenges for structural optimization approaches such as topology optimization (TO) since the number of variables to optimize increases with the resolutions. It also escalates the potential for high-resolution structure design. Advances in additive manufacturing enable the fabrication of complex structures with intricate geometric details.