Resolution In Regions Of Interest Research Articles

Direct numerical simulation of incompressible flows on parallel Octree grids

We introduce an approach for solving the incompressible Navier-Stokes equations on a forest of Octree grids in a parallel environment. The methodology uses the p4est library of Burstedde et al. (2011) [15] for the construction and the handling of forests of Octree meshes on massively parallel distributed machines and the framework of Mirzadeh et al. (2016) [54] for the discretizations on Octree data structures. We introduce relevant additional parallel algorithms and provide performance analyses for individual building bricks and for the full solver. We demonstrate strong scaling for the solver up to 32,768 cores for a problem involving O(6.1×108) computational cells. We illustrate the dynamic adaptive capabilities of our approach by simulating flows past a stationary sphere, flows due to an oscillatory sphere in a closed box and transport of a passive scalar. Without sacrificing accuracy nor spatial resolution in regions of interest, our approach successfully reduces the number of computational cells to (at most) a few percents of uniform grids with equivalent resolution. We also perform a numerical simulation of the turbulent flow in a superhydrophobic channel with unparalleled wall grid resolution in the streamwise and spanwise directions.

Adaptive fovea for scanning depth sensors

Depth sensors have been used extensively for perception in robotics. Typically these sensors have a fixed angular resolution and field of view (FOV). This is in contrast to human perception, which involves foveating: scanning with the eyes’ highest angular resolution over regions of interest (ROIs). We build a scanning depth sensor that can control its angular resolution over the FOV. This opens up new directions for robotics research, because many algorithms in localization, mapping, exploration, and manipulation make implicit assumptions about the fixed resolution of a depth sensor, impacting latency, energy efficiency, and accuracy. Our algorithms increase resolution in ROIs either through deconvolutions or intelligent sample distribution across the FOV. The areas of high resolution in the sensor FOV act as artificial fovea and we adaptively vary the fovea locations to maximize a well-known information theoretic measure. We demonstrate novel applications such as adaptive time-of-flight (TOF) sensing, LiDAR zoom, gradient-based LiDAR sensing, and energy-efficient LiDAR scanning. As a proof of concept, we mount the sensor on a ground robot platform, showing how to reduce robot motion to obtain a desired scanning resolution. We also present a ROS wrapper for active simulation for our novel sensor in Gazebo. Finally, we provide extensive empirical analysis of all our algorithms, demonstrating trade-offs between time, resolution and stand-off distance.

Scalable Wavelet-Based Coding of Irregular Meshes With Interactive Region-of-Interest Support

This paper proposes a novel functionality in wavelet-based irregular mesh coding, which is interactive region-of-interest (ROI) support. The proposed approach enables the user to define the arbitrary ROIs at the decoder side and to prioritize and decode these regions at arbitrarily high-granularity levels. In this context, a novel adaptive wavelet transform for irregular meshes is proposed, which enables: 1) varying the resolution across the surface at arbitrarily fine-granularity levels and 2) dynamic tiling, which adapts the tile sizes to the local sampling densities at each resolution level. The proposed tiling approach enables a rate-distortion-optimal distribution of rate across spatial regions. When limiting the highest resolution ROI to the visible regions, the fine granularity of the proposed adaptive wavelet transform reduces the required amount of graphics memory by up to 50%. Furthermore, the required graphics memory for an arbitrary small ROI becomes negligible compared to rendering without ROI support, independent of any tiling decisions. Random access is provided by a novel dynamic tiling approach, which proves to be particularly beneficial for large models of over 106 ~ 107 vertices. The experiments show that the dynamic tiling introduces a limited lossless rate penalty compared to an equivalent codec without ROI support. Additionally, rate savings up to 85% are observed while decoding ROIs of tens of thousands of vertices.

The scaling and skewness of optimally transported meshes on the sphere

In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to the success of these methods is that the mesh should be sufficiently refined (locally) and flexible in order to resolve evolving solution features, but at the same time not introduce errors through skewness and lack of regularity. Some state-of-the-art methods are bottom-up in that they attempt to prescribe both the local cell size and the alignment to features of the solution. However, the resulting problem is overdetermined, necessitating a compromise between these conflicting requirements. An alternative approach, described in this paper, is to prescribe only the local cell size and augment this an optimal transport condition to provide global regularity. This leads to a robust and flexible algorithm for generating meshes fitted to an evolving solution, with minimal need for tuning parameters. Of particular interest for geophysical modelling are meshes constructed on the surface of the sphere. The purpose of this paper is to demonstrate that meshes generated on the sphere using this optimal transport approach have good a-priori regularity and that the meshes produced are naturally aligned to various simple features. It is further shown that the sphere's intrinsic curvature leads to more regular meshes than the plane. In addition to these general results, we provide a wide range of examples relevant to practical applications, to showcase the behaviour of optimally transported meshes on the sphere. These range from axisymmetric cases that can be solved analytically to more general examples that are tackled numerically. Evaluation of the singular values and singular vectors of the mesh transformation provides a quantitative measure of the mesh anisotropy, and this is shown to match analytic predictions.

Frequency-banded nonlinear Schrödinger equation with inclusion of Raman nonlinearity.

The well-established generalized nonlinear Schrödinger equation (GNLSE) to simulate nonlinear pulse propagation in optical fibers and waveguides becomes inefficient if only narrow spectral bands are occupied that are widely separated in frequency/wavelength, for example in parametric amplifiers. Here we present a solution to this in the form of a coupled frequency-banded nonlinear Schrödinger equation (BNLSE) that only simulates selected narrow frequency bands while still including all dispersive and nonlinear effects, in particular the inter-band Raman and Kerr nonlinearities. This allows for high accuracy spectral resolution in regions of interest while omitting spectral ranges between the selected frequency bands, thus providing an efficient and accurate way for simulating the nonlinear interaction of pulses at widely different carrier frequencies. We derive and test our BNLSE by comparison with the GNLSE. We finally demonstrate the accuracy of the BNLSE and compare the computational execution times for the different models.

Single-shot full resolution region-of-interest (ROI) reconstruction in image plane digital holographic microscopy

We describe a numerical processing technique that allows single-shot region-of-interest (ROI) reconstruction in image plane digital holographic microscopy with full pixel resolution. The ROI reconstruction is modelled as an optimization problem where the cost function to be minimized consists of an L2-norm squared data fitting term and a modified Huber penalty term that are minimized alternately in an adaptive fashion. The technique can provide full pixel resolution complex-valued images of the selected ROI which is not possible to achieve with the commonly used Fourier transform method. The technique can facilitate holographic reconstruction of individual cells of interest from a large field-of-view digital holographic microscopy data. The complementary phase information in addition to the usual absorption information already available in the form of bright field microscopy can make the methodology attractive to the biomedical user community.

Teleoperated path following and trajectory tracking of unmanned vehicles using spatial auditory guidance system

The majority of Human–Machine Interfaces (HMIs) designed for the teleoperation of unmanned vehicles only present information visually. Frequent overloading of the operator’s visual channel may result in accidents. To reduce the occurrence of accidents and improve overall operating performance, this paper proposes the extension of the HMI to the hearing modality. The proposed HMI takes the form of a spatial auditory display for complex navigation tasks such as path following (route guidance) or trajectory tracking. The interface incorporates two novel components. The first is the application of a modified “lookahead distance” guidance strategy, as a guidance law for generating a reference. The reference is presented to the operator as a spatial auditory image of the virtual target to be followed. Before being presented to the operator, the reference information is preconditioned through “supernormal” transformations to increase azimuth and distance resolution in regions of interest and thus to improve efficiency and overcome the comparative disadvantages of the hearing channel. A series of experiments show that the proposed guidance strategy provides a comprehensible and effective auditory reference. The enhanced supernormal auditory interface improves performance by reducing the tracking error of both path following and trajectory tracking compared to a non-enhanced interface without the supernormal transformation. Experiment participants report that the novel auditory interface is intuitive and easy to use, providing very good situational awareness. While the auditory interface investigated in this paper is shown to be effective for the teleoperation of unmanned vehicles, it may have other applications such as navigation for the visually impaired.

BATCH CO-REGISTRATION OF MARS HIGH-RESOLUTION IMAGES TO HRSC MC11-E MOSAIC

Four NASA missions over the last forty years with onboard instruments for high-resolution orbital imaging have achieved both global coverage (with 6m CTX, 20m THEMIS-VIS and >8m Viking Orbiter cameras) as well as imaging with very high resolution in specific regions of interest (e.g. 25cm HiRISE and ≈1.5-12m MOC-NA cameras). Overall, this set of cameras have acquired more than 400,000 high-quality images of Mars with resolution between 25cm/pixel and 100m/pixel (Sidiropoulos and Muller, 2015). On the other hand, ESA has sent the only high-resolution stereo photogrammetric camera around Mars, HRSC onboard the Mars Express spacecraft, which has been mapping the Martian surface since 2004 with a resolution of 12.5 m/pixel (Jaumann et al., 2015). Initially the raw images are combined through an elaborate photogrammetric process to get (single-strip) 3D products (i.e. digital terrain models (DTMs) and derived orthorectified images (ORIs)). However, recently the processing chain has changed, and the single-strip product release was temporarily halted to be replaced by the production and release of mosaics of Mars quadrangles. The first product of this kind is the mosaic for the East part of quadrangle MC11 (i.e. the MC11-E mosaic), a product with 12.5 metres per pixel resolution in the panchromatic image and 50 metres per pixel resolution in the corresponding DTM (Gwinner et al., 2015). <br><br> Such a product provides an excellent basemap to co-register and orthorectify all NASA high-resolution (≤100m/pixel) orbital images. The need for this co-registration to HRSC comes from their poor areo-referencing, which often leads to large deviations (reaching up to several kilometres) between the area they are supposed to image and the area they are actually imaging. After co-registration, all products are projected onto an common 3D coordinate system, which allows an examination of dynamic features of Mars through the changes that happen on its surface. In this work, we present the results of the batch coregistration of all NASA high-resolution orbiter images of MC11-E, i.e. almost 8,000 images in total. This task was conducted with an in-house pipeline which was modified in order to handle the different parameters of the mosaic in comparison to single-strip HRSC products and to process the large input data volumes within a realistic time. An outline of the processing pipeline is given, along with examples of co-registered images and statistics of the co-registration performance. We demonstrate how such a time series representation of the surface will open up new areas for exploration and understanding of the Martian surface.

EBits: Compact stream of mesh refinements for remote visualization

We focus on applications where a remote client needs to visualize or process a complex, manifold triangle mesh, M, but only in a relatively small, user controlled, Region of Interest (RoI) at a time. The client first downloads a coarse base mesh, pre-computed on the server via a series of simplification passes on M, one per Level of Detail (LoD), each pass identifying an independent set of triangles, collapsing them, and, for each collapse, storing, in a Vertex Expansion Record (VER), the information needed to reverse the collapse. On each client initiated RoI modification request, the server pushes to the client a selected subset of these VERs, which, when decoded and applied to refine the mesh locally, ensure that the portion in the RoI is always at full resolution. The eBits approach proposed here offers state of the art compression ratios (using less than 2.5 bits per new full resolution RoI triangle when the RoI has more than 2000 vertices to transmit the connectivity for the selective refinements) and fine-grain control (allowing the user to adjust the RoI by small increments). The effectiveness of eBits results from several novel ideas and novel variations of previous solutions. We represent the VERs using persistent labels so that they can be applied in different orders within a given LoD. The server maintains a shadow copy of the client’s mesh. To avoid sending IDs identifying which vertices should be expanded, we either transmit, for each new vertex, a compact encoding of its death tag ​–the LoD at which it will be expanded if it lies in the RoI–or transmit vertex masks for the RoI and its neighboring vertices. We also propose a three-step simplification that reduces the overall transmission cost by increasing both the simplification effectiveness and the regularity of the valences in the resulting meshes.

ROI-Based Image Reconstruction of Electrical Impedance Tomography Used to Detect Regional Conductivity Variation

The advantages of noninvasive, fast speed, low-cost, and nonionizing radiation hazard have made electrical impedance tomography (EIT) an attractive imaging technology in geological, medical, and industrial applications. However, the EIT image has low spatial resolution due to the limited number of independent measurements and soft-field property. Focused on the fact that, in some applications, the conductivity variation exists only in part of the sensing field, this paper proposes a new strategy to enhance the image quality by restricting the image reconstruction within a region of interest (RROI). Compared with the conventional image reconstruction over the entire sensing field, the proposed strategy of RROI can improve regional image resolution effectively without increasing the number of electrodes and the complexity of the data acquisition system. The implementation of a conventional sensitivity-theorem-based conjugate gradient algorithm with the proposed RROI strategy is presented, and the improvement of image spatial resolution in region of interest is demonstrated by both simulations and phantom experiments.

Oil Spill Models: A State of the Art of the Grid Map as a Function of Wind, Current and Oil Parameters

An integrated model, which contains flow and transport-fate modules, will be presented for simulating transport and fate of oil spills at seas. The flow module uses different kinds of meshes that provide great flexibility for modeling the flow in complex geometries of currents and barriers. The refined grid resolution in regions of interest is important. Horizontal diffusion is simulated using random walk techniques in a Monte Carlo framework, whereas the vertical diffusion process can be solved on the basis of the Langeven equation. The model contains the most significant processes which affect the motion of oil particles. For a better fit to the curvature of the coastline there are used unstructured non overlapping rectangular or triangle grid cells. Special attention must be paid to choose the horizontal and vertical resolution in simulating the oil trajectory in the coastal area.

SU-E-I-99: An Ultra-High Resolution Small Field-Of-View Solid State X-Ray Imaging Detector Based on an Electron Multiplying CCD.

To demonstrate the ultra-high resolution capability of a small field-of-view (FOV) solid state x-ray imaging detector based on an EMCCD sensor. A micro-solid state x-ray image intensifier (micro-SSXII) was developed to serve as an ultra-high resolution region-of-interest (ROI) imaging detector. It is based on an 8 micron, 1004 by 1002 pixel electron multiplying CCD (EMCCD) optically coupled to a 100 micron thick CsI(Tl) phosphor through a fiber optic window resulting in a FOV of 8 mm. The modulation transfer function (MTF) of the micro-SSXII was measured by the slanted edge method. A cast of a rat kidney (made by mixing resin and iodine for contrast) and a mammography line pair test object were imaged at 50 kVp to demonstrate the detector's ultra-high resolution capability visually. The MTF was determined and was 5% at 20 cycles/mm. This is consistent with the clear visualization of the maximum 20 lp/mm group in the image of the mammography test object. Also, iodine bubbles with diameters as small as 25 microns, which are formed by the non-uniform mixing of the iodine in the resin cast, can be clearly identified in the rat kidney vessels. The ultra-high resolution capability (>20 lp/mm) but small FOV (8 mm) of the micro-SSXII in combination with a low-energy x-ray source may have application for investigations of vascular specimen details and other fine structures where optical or other surface imagers would be unsuited for evaluating features below the surface. Contact radiography with this imager combined with a large higher-load focal spot x-ray tube may be a promising substitute for magnification radiography which is limited by the use of specialized low output microfocus x-ray tubes and geometric un-sharpness for large magnifications. Supported in part by: NIH Grants R01-EB008425, R01-EB002873 and an equipment grant from Toshiba Medical Systems Corp.

In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration.

Recently, spatial encoding with nonlinear magnetic fields has drawn attention for its potential to achieve faster gradient switching within safety limits, tailored resolution in regions of interest, and improved parallel imaging using encoding fields that complement the sensitivity profiles of radio frequency receive arrays. Proposed methods can broadly be divided into those that use phase encoding (Cartesian-trajectory PatLoc and COGNAC) and those that acquire nonlinear projections (O-Space, Null space imaging, radial PatLoc, and 4D-RIO). Nonlinear projection data are most often reconstructed with iterative algorithms that backproject data using the full encoding matrix. Just like conventional radial sequences that use linear spatial encoding magnetic fields, nonlinear projection methods are more sensitive than phase encoding methods to imperfect calibration of the encoding fields. In this work, voxel-wise phase evolution is mapped at each acquired point in an O-Space trajectory using a variant of chemical shift imaging, capturing all spin dynamics caused by encoding fields, eddy currents, and pulse timing. Phase map calibration is then applied to data acquired from a high-power, 12 cm, Z2 insert coil with an eight-channel radio frequency transmit-receive array on a 3T human scanner. We show the first experimental proof-of-concept O-Space images on in vivo and phantom samples, paving the way for more in-depth exploration of O-Space and similar imaging methods.

Development and validation of a three-dimensional, wave-current coupled model on unstructured meshes

Using unstructured meshes provides great flexibility for modeling the flow in complex geomorphology of tidal creeks, barriers and islands, with refined grid resolution in regions of interest and not elsewhere. In this paper, an unstructured three-dimensional fully coupled wave-current model is developed. Firstly, a parallel, unstructured wave module is developed. Variations in wave properties are governed by a wave energy equation that includes wave-current interactions and dissipation representative of wave breaking. Then, the existing Finite-Volume Coastal Ocean Model (FVCOM) is modified to couple with the wave module. The couple procedure includes depth dependent wave radiation stress terms, Stokes drift, vertical transfer of wave-generated pressure transfer to the mean momentum equation, wave dissipation as a source term in the turbulence kinetic energy equation, and mean current advection and refraction of wave energy. Several applications are presented to evaluate the developed model. In particular the wind and wave-induced storm surge generated by Hurricane Katrina is investigated. The obtained results have been compared to the in situ measurements with respect to the wave heights and water level elevations revealing good accuracy of the model in reproduction of the investigated events. In a comparison to water level measurements at Dauphin Island, inclusion of the wave induced water level setup reduced the normalized root mean square error from 0.301 to 0.257 m and increased the correlation coefficient from 0.860 to 0.929. Several runs were carried out to analyze the effects of waves. The experiments show that among the processes that represent wave effects, radiation stress and wave-induced surface stress are more important than wave-induced bottom stress in affecting the water level. The Hurricane Katrina simulations showed the importance of the inclusion of the wave effects for the hindcast of the water levels during the storm surge.

Modeling oil spills transportation in seas based on unstructured grid, finite-volume, wave-ocean model

A three-dimensional integrated model is developed for simulating transport and fate of oil spills in seas. The model contains two main modules, flow and transport-fate modules. The flow module uses an unstructured finite-volume wave-ocean coupling model. Using unstructured meshes provides great flexibility for modeling the flow in complex geometries of tidal creeks, barriers and islands, with refined grid resolution in regions of interest and not elsewhere. In the transport-fate module the oil dispersion is solved using a particle-tracking method. Horizontal diffusion is simulated using random walk techniques in a Monte Carlo framework, whereas the vertical diffusion process is solved on the basis of the Langeven equation. The model simulates the most significant processes that affect the motion of oil particles, such as advection, surface spreading, evaporation, dissolution, emulsification and turbulent diffusion as well as the interaction of the oil particles with the shoreline, sedimentation and the temporal variations of oil viscosity, density and surface-tension. Detailed comparisons of simulations with analytical solutions and numerical simulations made with the popular structured finite difference model ROMS (the Regional Ocean Modeling System) for two idealized cases: wind-induced long-surface gravity waves in a circular lake and freshwater discharge onto the continental shelf with curved coastlines, are presented. With a better fit to the curvature of the coastline using unstructured nonoverlapping triangle grid cells, the developed model system provides improved numerical accuracy in simulating the oil spill trajectory. Also keep in mind that attention must be paid to choose the horizontal and vertical resolution in simulating the oil trajectory in the coastal ocean.

Correlating nerve fibre layer defects spatially with functional loss

The ultimate aim of clinical glaucoma research is to maintain visual function in the patient. Visual field (VF) loss can be determined more effectively by considering the related structural damage (ie retinal nerve fibre layer (RNFL) defect, optic disc notching, and splinter haemorrhages). A stack of individually digitized RNFL traces, which are superimposed by appropriate rotation and zoom procedures, allows for characterizing so-called trajectories defining the average course of retinal nerve fibres.Individual test point density in perimetry can be increased in regions of interest, that is in areas, or at the edges of, already detected VF defects (VFD) using SCotoma-Oriented Perimetry (SCOPE) or can be tailored (locally condensed) in an evidence-based manner by considering the local morphological damage using fundus-oriented perimetry (FOP). Focusing on areas most likely to be damaged makes conventional perimetry more efficient by locally enhancing spatial resolution. This technique requires a mathematical model that provides age-related normative values of differential luminance sensitivity for any location of the VF. Automated static perimetry with enhancement of spatial resolution in regions of interest has indeed a higher sensitivity than standard automated perimetry using a conventional rectangular (6 × 6°) grid. The new method can also be used for follow-up purposes: both scotoma depth and area, as well as their changes with time, need to be considered. The clinician has to be aware of the fact that any kind of perimetry is a rather exhausting and artificial examination procedure. It is rather inadequate for predicting per sepatients' quality of life and daily functionality as it does not consider compensation for VFD, for example by gaze and head movements.

Diagnosis of an interstitial pregnancy with 4-dimensional volume contrast imaging

The purpose of this study was to investigate the use of a new ultrasound technique, termed 4-dimensional volume contrast imaging in coronal-plane to facilitate the early detection of interstitial pregnancy. A case of interstitial pregnancy was diagnosed accurately at 6 weeks of gestation with 4-dimensional transvaginal volume contrast imaging in coronal plane technology. A scan of the uterus revealed that the eccentric gestational sac was located in the right uterotubal junctional area, lying 1 cm outside the most upper lateral edge of the uterine cavity with thick endometrial echoes. After the appropriate counseling, the patient was treated with an ultrasonographically guided intracardiac injection of 2.5 mEq of potassium chloride followed by aspiration of the gestational sac. A transvaginal scan immediately after the procedure demonstrated a collapsed empty gestational sac. Three months after the conservative treatment, the serum beta-human chorionic gonadotropin level fell to 1.17 mIU/mL, and normal echotexture of the uterus was noted. Four-dimensional volume contrast imaging in coronal-plane technology provides scan planes that are not accessible by conventional 2-dimensional scanning, with enhanced tissue contrast resolution in region of interest. This new ultrasound technique has the potential to provide more accurate, inexpensive and less variable virtual reality image-guided interventional options through more realistic interaction with the virtualized in utero condition, particularly when 2-dimensional transvaginal scan fails to differentiate between interstitial, angular, and cornual pregnancies.

Optimal time-activity basis selection for exponential spectral analysis: application to the solution of large dynamic emission tomographic reconstruction problems

The clinical application of dynamic ECT reconstruction algorithms for inconsistent projection (IP) data has been beset with difficulties. These include poor scalability, numerical instability of algorithms, problems of nonuniqueness of solutions, the need to oversimplify tracer kinetics, and impractical computational burden. The authors present a stable reconstruction algorithm with low computational cost that is able to recover the tracer kinetics of several hundred image regions at realistic noise levels. Through optimal selection of a small set of nonnegative basis functions to describe regional time-activity curves (TACs), the authors are able to solve for the first-order compartmental model kinetics of each region. A nonuniform resolution pixelization of image space is employed to obtain highest resolution in regions of interest. These spatial and temporal simplifications improve numerical conditioning, provide robustness against noise, and greatly decrease the computational burden of dynamic reconstruction. The authors apply this algorithm to IP phantom data whose source distribution, kinetics, and count statistics are modeled after a clinical myocardial SPECT dataset. TACs of phantom regions are recovered to within a mean square error of 6%, an accuracy that proves sufficient to allow for quantitative detection of a myocardial perfusion defect within healthy myocardial tissue.

A new 3D FDTD multigrid technique with dielectric traverse capabilities

The finite-difference time-domain (FDTD) technique has become increasingly popular and is being used to model extremely complex and electrically large structures. These simulations are computationally demanding and often exceed available limits on computer resources. In this paper, we present an FDTD sub-gridding technique that allows for increased resolution in regions of interest without increasing the overall computational requirements beyond the available resources. Furthermore, the formulation presented here allows for traversing dielectric boundaries using any integer refinement factor and the maximum Courant number. By allowing the coarse-/fine-grid boundary to traverse dielectric boundaries, numerical simulations that were previously either extremely difficult or impossible to perform are now possible. The technique presented here uses a weighted current value from the coarse region at the boundary between the fine- and coarse-grid regions to update the fine-region tangential fields on that boundary. The weighting function depends on the material properties and the relative position of the fine-region electric field within the current contour at the boundary. The complete formulation of this new technique is described and some results of simulation cases are presented to validate the accuracy and stability of the newly developed FDTD code. Simulations include simple cases where the analytical solution exists and more complex cases, which were impossible to model using a uniform-grid FDTD code. In some simulation examples, computer memory savings as high as 70 times what would have been necessary with a uniform-grid code were achieved. It is shown that errors of less than 2% are achievable with ratios of coarse-to-fine grid sizes exceeding ten. The new technique is expected to be used in simulating many electrically large and complex structures in the biomedical microwave processing of materials and the wireless communications areas.