Ruinan Chang

FastMag: Fast micromagnetic simulator for complex magnetic structures (invited)

A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle problems of a small or very large size with a high speed. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel Graphics Processing Unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus discretized superposition integrals are computed using a non-uniform grid interpolation method, which evaluates the field from N sources at N collocated observers in ( ) O N operations. This approach allows handling any uniform or non-uniform shapes, allows easily calculating the field outside the magnetized domains, does not require solving linear system of equations, and requires little memory. FastMag is implemented on GPUs with GPU-CPU speed-ups of two orders of magnitude. Simulations are shown of a large array and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.

Fast Electromagnetic Integral-Equation Solvers on Graphics Processing Units

A survey of electromagnetic integral-equation solvers, implemented on graphics processing units (GPUs), is presented. Several key points for efficient GPU implementations of integral-equation solvers are outlined. Three spatial-interpolation-based algorithms, including the Nonuniform-Grid Interpolation Method (NGIM), the box Adaptive-Integral Method (B-AIM), and the fast periodic interpolation method (FPIM), are described to show the basic principles for optimizing GPU-accelerated fast integral-equation algorithms. It is shown that proper implementations of these algorithms lead to very high computational performance, with GPU-CPU speed-ups in the range of 100-300. Critical points for these accomplishments are (i) a proper arrangement of the data structure, (ii) an “on-the-fly” approach, trading excessive memory usage with increased arithmetic operations and data uniformity, and (iii) efficient utilization of the types of GPU memory. The presented methods and their GPU implementations are geared towards creating efficient electromagnetic integral-equation solvers. They can also find a wide range of applications in a number of other areas of computational physics.

Advanced Micromagnetic Analysis of Write Head Dynamics Using Fastmag

Magnetization and magnetic field dynamics arising when switching a realistic recording head model is studied. The write head design comprises a return pole, yoke, main pole, tapered trapezoidal pole tip, tapered wrap around shield (WAS), and soft underlayer. The analysis was performed using the high-performance micromagnetic simulator FastMag, which is well suited for the write head dynamic problems due to its ability to handle complex magnetic devices discretized into many millions of elements. The head dynamics is considered for different mesh densities, switching data rates, and current waveforms. It is demonstrated that improper discretization may result in a very different magnetization behavior. This is especially pronounced for cases of high switching rates, for which meshes of insufficient density resulted in a completely incorrect behavior, e.g. absence of switching. On the other hand, sufficiently dense meshes resulted in reliable dynamics and switching behavior. Furthermore, magnetization dynamics effects in WAS and their effects on the magnetostatic fields in the media layer were studied. WAS significantly improves the head field gradients in both down- and off-track directions, which is important for high areal recording densities. However, the presence of WAS leads to reduced write fields below the pole tip and to significant undesired magnetostatic fields below the side shields in the media layer. Such undesired fields can be obtained close to the pole tip as well as far from the tip. These phenomena result from the domain wall creation, propagation, and annihilation in WAS due to the switching. The field close to the pole tip can result in adjacent track erasure, while fields far from the tip can lead to far track erasure. The existence of these fields should be accounted for when performing recording system design optimization and analysis.

Micromagnetics on high-performance workstation and mobile computational platforms

The feasibility of using high-performance desktop and embedded mobile computational platforms is presented, including multi-core Intel central processing unit, Nvidia desktop graphics processing units, and Nvidia Jetson TK1 Platform. FastMag finite element method-based micromagnetic simulator is used as a testbed, showing high efficiency on all the platforms. Optimization aspects of improving the performance of the mobile systems are discussed. The high performance, low cost, low power consumption, and rapid performance increase of the embedded mobile systems make them a promising candidate for micromagnetic simulations. Such architectures can be used as standalone systems or can be built as low-power computing clusters.

Large exchange-dominated domain wall velocities in antiferromagnetically coupled nanowires

Magnetic nanowires supporting field- and current-driven domain wall motion are envisioned for methods of information storage and processing. A major obstacle for their practical use is the domain-wall velocity, which is traditionally limited for low fields and currents due to the Walker breakdown occurring when the driving component reaches a critical threshold value. We show through numerical and analytical modeling that the Walker breakdown limit can be extended or completely eliminated in antiferromagnetically coupled magnetic nanowires. These coupled nanowires allow for large domain-wall velocities driven by field and/or current as compared to conventional nanowires.

Quadrilateral Barycentric Basis Functions for Surface Integral Equations

A framework for solving surface integral equation on quadrilateral, triangular, and mixed quadrilateral-triangular meshes is presented. The initial meshes are represented in terms of quadrilateral barycentric meshes (QBMs), which are obtained by partitioning each initial quadrilateral and triangle into four and three barycentric quadrilaterals, respectively. Quadrilateral barycentric basis functions (QBBFs) are defined on QBMs. The QBBFs serve a dual role. First, they allow defining primary basis functions (PBFs), which are well suited for representing surface currents on quadrilateral, triangular, and mixed meshes. Second, the QBBFs are used to define dual basis function (DBFs), which are natural for using in conjunction with Calderón multiplicative preconditioners (CMPs). These QBBFs, PBFs, and DBFs result in a substantial reduction in the number of nonzero elements in the sparse projection matrices for PBFs and DBFs as well as reduction of unknowns and quadrature points. When these PBFs and DBFs are used in CMPs, they reduce the number of iterations and eliminate the dense mesh breakdown of the surface electric field integral equation. Numerical examples demonstrate the efficiency of using the introduced QBBFs with associated PBFs and DBFs for solving electromagnetic surface electric field integral equations on quadrilateral, triangular, and mixed meshes.

Potential-based volume integral equations

Electromagnetic potential-based volume integral equations (VIEs) for the efficient analysis of large-scale problems are presented. Different from the conventional VIEs the proposed approach is based on scalar and vector potential unknowns. A VIE and the Lorentz gauge equations constitute a complete required set. The introduced potential VIEs (PVIEs) allow using scalar interpolatory nodal basis functions, do not require any surface integrals (both for homogeneous or inhomogeneous domains), and do not involve any hyper-singular integrals. This method works from very low- to high-frequency regimes, does not have high-density mesh breakdowns, requires a significantly reduced number of quadrature nodes as compared to methods based on vector basis functions, and is easy to implement for low- and high-order basis functions. The method is coupled with fast interpolation based techniques implemented on Graphics Processing Units (GPUs) to allow for the rapid analysis of complex structures.

Coupling electromagnetics with micromagnetics

A time domain simulator for analyzing non-linear coupled electromagnetic and micromagnetic phenomena in complex magnetic structures is introduced. The simulator employs a new integral formulation that accurately accounts for the Eddy currents and captures the dominant physics. An implicit time stepping scheme that uses an analytic Jacobian method and allows for large time steps is proposed. Finally, the simulator has a low (O(N logN)) computational complexity for a system with N mesh elements and it is implemented on massively parallel GPU computing systems, which permits for the rapid analysis of highly complex magnetic devices.

Numerical modeling of heat assisted magnetic recording system

Heat assisted magnetic recording (HAMR) is envisioned as the next technology for boosting the recording densities. In HAMR, a localized optical field is used to locally heat the magnetic recording media layer, thus reducing the thermal stability and allowing recording at sufficiently weak magnetic fields. After cooling down, the recording layer restores the original high thermal stability. From the simulation point of view HAMR requires integrated modeling approaches, including magnetics, optics, heat transport, and electromagnetics.

Accurate evaluation of exchange fields in finite element micromagnetic solvers

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.