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At least 541 records · Page 30
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NASA NTRS2000

Polar Spacecraft Based Comparisons of Intense Electric Fields and Poynting Flux Near and Within the Plasma Sheet-Tail Lobe Boundary to UVI Images: An Energy Source for the Aurora

In this paper, we present measurements from two passes of the Polar spacecraft of intense electric and magnetic field structures associated with Alfven waves at and within the outer boundary of the plasma sheet at geocentric distances of 4-6 R(sub E), near local midnight. The electric field variations have maximum values exceeding 100 mV/m and are typically polarized approximately normal to the plasma sheet boundary. The electric field structures investigated vary over timescales (in the spacecraft frame.) ranging front 1 to 30 s. They are associated with strong magnetic field fluctuations with amplitudes of 10-40 nT which lie predominantly ill the plane of the plasma sheet and are perpendicular to the local magnetic field. The Poynting flux associated with the perturbation fields measured at these altitudes is about 1-2 ergs per square centimeters per second and is directed along the average magnetic field direction toward the ionosphere. If the measured Poynting flux is mapped to ionospheric altitudes along converging magnetic field lines. the resulting energy flux ranges up to 100 ergs per centimeter squared per second. These strongly enhanced Poynting fluxes appear to occur in layers which are observed when the spacecraft is magnetically conjugate (to within a 1 degree mapping accuracy) to intense auroral structures as detected by the Polar UV Imager (UVI). The electron energy flux (averaged over a spatial resolution of 0.5 degrees) deposited in the ionosphere due to auroral electron beams as estimated from the intensity in the UVI Lyman-Birge-Hopfield-long filters is 15-30 ergs per centimeter squared per second. Thus there is evidence that these electric field structures provide sufficient Poynting flux to power the acceleration of auroral electrons (as well as the energization of upflowing ions and Joule heating of the ionosphere). During some events the phasing and ratio of the transverse electric and magnetic field variations are consistent with earthward propagation of Alfven surface waves with phase velocities of 4000-10000 kilometers per second. During other events the phase shifts between electric and magnetic fields suggest interference between upward and downward propagating Alfven waves. The E/B ratios are about an order of magnitude larger than typical values of C/SIGMA(sub p), where SIGMA(sub p), is the height integrated Pedersen conductivity. The contribution to the total energy flux at these altitudes from Poynting flux associated with Alfven waves is comparable to or larger than the contribution from the particle energy flux and 1-2 orders of magnitude larger than that estimated from the large-scale steady state convection electric field and field-aligned current system.

Wygant, J. R.↗
NASA NTRS2001

Determining Greenland Ice Sheet Accumulation Rates from Radar Remote Sensing

An important component of NASA's Program for Arctic Regional Climate Assessment (PARCA) is a mass balance investigation of the Greenland Ice Sheet. The mass balance is calculated by taking the difference between the snow accumulation and the ice discharge of the ice sheet. Uncertainties in this calculation include the snow accumulation rate, which has traditionally been determined by interpolating data from ice core samples taken throughout the ice sheet. The sparse data associated with ice cores, coupled with the high spatial and temporal resolution provided by remote sensing, have motivated scientists to investigate relationships between accumulation rate and microwave observations.

Jezek, Kenneth C.↗
NASA NTRS2003

Understanding Recent Mass Balance Changes of the Greenland Ice Sheet

The ultimate goal of this project is to better understand the current transfer of mass between the Greenland Ice Sheet, the world's oceans and the atmosphere, and to identify processes controlling the rate of this transfer, to be able to predict with greater confidence future contributions to global sea level rise. During the first year of this project, we focused on establishing longer-term records of change of selected outlet glaciers, reevaluation of mass input to the ice sheet and analysis of climate records derived from ice cores, and modeling meltwater production and runoff from the margins of the ice sheet.

vanderVeen, Cornelius↗
NASA NTRS2003

Modeling Primary Breakup: A Three-Dimensional Eulerian Level Set/Vortex Sheet Method for Two-Phase Interface Dynamics

This paper is divided into four parts. First, the level set/vortex sheet method for three-dimensional two-phase interface dynamics is presented. Second, the LSS model for the primary breakup of turbulent liquid jets and sheets is outlined and all terms requiring subgrid modeling are identified. Then, preliminary three-dimensional results of the level set/vortex sheet method are presented and discussed. Finally, conclusions are drawn and an outlook to future work is given.

Herrmann, M.↗
NASA NTRS2005

Current Sheet Evolution in the Aftermath of a CME Event

We report on SOHO-UVCS observations of the coronal restructuring following a Coronal Mass Ejection (CME) on November 26,2002, at the time of a SOHO-Ulysses quadrature campaign. Starting about 3 hours after a CME in the NW quadrant, UVCS began taking spectra at 1.7 solar radius, covering emission from both cool and hot plasma. Observations continued, with occasional gaps, for more than 2 days. Emission in the 974.8 Angstrom line of [Fe XVIII], indicating temperatures above 6 x 10(exp 6) K, was observed throughout the campaign in a spatially limited location. Comparison with EIT images shows the Fe XVIII emission to overlie a growing post-flare loop system formed in the aftermath of the CME. The emission most likely originates in a current sheet overlying the arcade. Analysis of the [Fe XVIII] emission allows us to infer the evolution of physical parameters in the current sheet over the entire span of our observations: in particular, we give the temperature vs. time in the current sheet and estimate the density. At the time of the quadrature, Ulysses was directly above the location of the CME and intercepted the ejecta. High ionization state Fe was detected by Ulysses-SWICS throughout the magnetic cloud associated with the CME. Both the remote and in situ observations are compared with predictions of theoretical CME models.

Bemporad, A.↗
NASA NTRS2005

Graphite Sheet Coating for Improved Thermal Oxidative Stability of Carbon Fiber Reinforced/PMR-15 Composites

Expanded graphite was compressed into graphite sheets and used as a coating for carbon fiber reinforced PMR-15 composites. BET analysis of the graphite indicated an increase in graphite pore size on compression, however the material was proven to be an effective barrier to oxygen when prepegged with PMR-15 resin. Oxygen permeability of the PMR-15/graphite was an order of magnitude lower than the compressed graphite sheet. By providing a barrier to oxygen permeation, the rate of oxidative degradation of PMR-15 was decreased. As a result, the composite thermo-oxidative stability increased by up to 25%. The addition of a graphite sheet as a top ply on the composites yielded little change in the material's flexural strength or interlaminar shear strength.

Campbell, Sandi↗
NASA NTRS2003

Sheet Flows, Avalanches, and Dune Evolution on Earth and Mars

This investigation is a collaboration between researchers at Cornell University, the University of Florida, and the University of Rennes 1, France. Flow modeling at Cornell University focused on mechanisms for the suspension and transport of wind-blown sand that are important in both terrestrial and Martian environments. These mechanisms include the saltation (or jumping) of grains, collisions between grains, and the interaction of grains with the velocity fluctuations of the turbulent wind. Of particular interest are sheet flows; these are relatively thin, highly concentrated regions of grains flowing near the ground under the influence of a strong turbulent wind. In them, the grains are suspended by interparticle collisions. Sheet flows may be relatively rare events, but they have the capacity to move great amounts of sand. In order to describe sheet flows, a turbulent mixture theory was formulated for particles in a fluid in which fluctuations in the volume fiaction of the particles take place on the scale of the turbulent eddies. Ensemble averaged equations for particle and fluid mass, momentum, and energy and fluid rate of dissipation were expressed in terms of Farve (concentration) averaged velocities and the associated velocity fluctuations. Correlations that describe the turbulent suspension of particles and dissipation of turbulent energy of both phases due to fluid particle interactions were modeled and boundary conditions at the bed and at the upper surface of the collisional flow were formulated. The boundary conditions at the upper surface were tested in a numerical simulation developed at the University of Florida. Steady and unsteady solutions for steady and unsteady fully-developed flows were obtained over a range of wind speeds fiom the lowest for which collisional between particles occurred to at which turbulent suspension is found to dominate collisional suspension. Below the value of the wind speed at which collisions between particles were unimportant, numerical solutions were obtained for the velocity distribution function and the resulting fields of concentration, particle and gas mean velocity, and particle shear stress for the steady two-dimensional saltation of spherical sand particles driven by a turbulent wind over a bed characterized by a simple relationship (the splash function) between the properties of incoming particles and those of the rebounding particles and other particles ejected fiom the bed. At the University of Rennes 1, experiments devoted to the characterization of the splash function for beds consisting of either random or ordered arrays of spheres in two- dimensions were completed. These indicated the role played by the packing geometry in the rebound and ejection of grains. Preliminary experiments on response of a three- dimensional collision bed to a collision with a single particle were performed. Data was taken with a single camera focused on the plane of collision. Here, for example, the decrease of the effective coefficient of restitution of the bed with an increase of the angle of incidence of the incoming particle has been measured. Other experiments on avalanches at Rennes studied the properties of the flows of particles that are responsible for the motion of the leeward side of a dune. In these, the dependence of the initiation of avalanches on the packing and depth of the particles was measured. Particle migration was studied in inclined flows of a binary mixture of disks and the mechanisms of diffision and segregation were isolated and characterized. The influence of side wall on dense, rapid inclined flows was measured and shown to be the reason why the angle of the free surface in such flows can exceed the static angle of repose. Future research will be devoted to a better understanding the transition between saltating (collisionless) and collisional flows as the wind speed the increases. This will involve the understanding of the evolution of the splash function as clisions with the bed become more numerous, more frequent, and more violent.

Source record↗
NASA NTRS2006

The Role of Current Sheets in Solar Eruptive Events: An ISSI International Team Project

Current sheets (CSs) are a prerequisite for magnetic reconnection. An International Space Science Institute (ISSI, of Bern, Switzerland) research team will work to empirically define current sheet properties in the solar atmosphere and their signatures in the interplanetary medium, and to understand their role in the development of solar eruptive events. The project was inspired by recently acquired ground and space based observations that reveal CS signatures at the time of flares and Coronal Mass Ejections (CMEs), in the chromosphere, in the corona and in the interplanetary medium. At the same time, theoretical studies predict the formation of CSs in different models and configurations, but theories and observational results have not yet developed an interaction efficient enough to allow us to construct a unified scenario. The team will generate synergy between observers, data analysts, and theoreticians, so as to enable a significant advance in understanding of current sheet behavior and properties. A further motivation for studying CSs is related to the expected electric fields in CSs that may be the source of solar energetic particles (SEPs). The team has 14 members from Europe and the US. The first meeting is in October 2006 and the second is late in 2007.

Suess, Steven T.↗
NASA NTRS2008

Recent Ice Sheet and Glacier Elevation Changes in Greenland from Aircraft Laser Altimetry

The Arctic Ice Mapping group (Project AIM) at the NASA Goddard Space Flight Center Wallops Flight Facility has been conducting systematic topographic surveys of the Greenland Ice Sheet (GIS) since 1993, using scanning airborne laser altimeters combined with Global Positioning System (UPS) technology. Earlier surveys showed the ice sheet above 2000-rn elevation to be in balance, but with localized regions of thickening or thinning. Thinning predominates at lower elevations and thinning rates have recently increased, resulting in a negative mass balance for the entire ice sheet. Recently, critical segments of near-coastal flight lines in Greenland were resurveyed. Results from the new data will be presented.

Krabill, William B.↗
NASA NTRS2009

Morphology and Density Structure of Post-CME Current Sheets

Eruption of a coronal mass ejection (CME) is believed to drag and open the coronal magnetic field, presumably leading to the formation of a large-scale current sheet and field relaxation by magnetic reconnection. This paper analyzes the physical characteristics of ray-like coronal features formed in the aftermath of CMEs, to confirm whether interpreting such phenomena in terms of a reconnecting current sheet is consistent with observations. Methods: The study focuses on UVCS/SOHO and LASCO/SOHO measurements of the ray width, density excess, and coronal velocity field as a function of the radial distance. The morphology of the rays implies that they are produced by Petschek-like reconnection in the large-scale current sheet formed in the wake of CME. The hypothesis is supported by the flow pattern, often showing outflows along the ray, and sometimes also inflows into the ray. The inferred inflow velocities range from 3 to 30 km/s, and are consistent with the narrow opening-angle of rays, which add up to a few degrees. The density of rays is an order of magnitude higher than in the ambient corona. The model results are consistent with the observations, revealing that the main cause of the density excess in rays is a transport of the dense plasma from lower to higher heights by the reconnection outflow.

Vrsnak, B.↗
NASA NTRS2009

A Climate-Data Record of the "Clear-Sky" Surface Temperature of the Greenland Ice Sheet

We are developing a climate-data record (CDR of daily "clear-sky" ice-surface temperature (IST) of the Greenland Ice Sheet, from 1982 to the present using Advanced Very High Resolution Radiometer (AVHRR) (1982 - present) and Moderate-Resolution Imaging Spectroradiometer (MODIS) data (2000 - present) at a resolution of approximately 5 km. The CDR will be continued in the National Polar-orbiting Operational Environmental Satellite System Visible/Infrared Imager Radiometer Suite era. Two algorithms remain under consideration. One algorithm under consideration is based on the split-window technique used in the Polar Pathfinder dataset (Fowler et al., 2000 & 21007). Another algorithm under consideration, developed by Comiso (2006), uses a single channel of AVHRR data (channel 4) in conjunction with meteorological-station data to account for atmospheric effects and drift between AVHRR instruments. Known issues being addressed in the production of the CDR are: tune-series bias caused by cloud cover (surface temperatures can be different under clouds vs. clear areas) and cross-calibration in the overlap period between AVHRR instruments, and between AVHRR and MODIS instruments. Because of uncertainties, mainly due to clouds (Stroeve & Steffen, 1998; Wang and Key, 2005; Hall et al., 2008 and Koenig and Hall, submitted), time-series of satellite 1S'1" do not necessarily correspond to actual surface temperatures. The CDR will be validated by comparing results with automatic-,",eather station (AWS) data and with satellite-derived surface-temperature products. Regional "clear-sky" surface temperature increases in the Arctic, measured from AVHRR infrared data, range from 0.57+/-0.02 deg C (Wang and Key, 2005) to 0.72+/-0.10 deg C (Comiso, 2006) per decade since the early 1980s. Arctic warming has important implications for ice-sheet mass balance because much of the periphery of the Greenland Ice Sheet is already near 0 deg C during the melt season, and is thus vulnerable to rapid melting if temperatures continue to increase. References

Hall, D. K.↗
NASA NTRS2011

A Climate-Data Record (CDR) of the "Clear Sky" Surface Temperature of the Greenland Ice Sheet

To quantify the ice-surface temperature (IST) we are developing a climate-data record (CDR) of monthly IST of the Greenland ice sheet, from 1982 to the present using Advanced Very High Resolution Radiometer (AVHRR) and Moderate-Resolution Imaging Spectroradiometer (MODIS) data at 5-km resolution. "Clear-sky" surface temperature increases have been measured from the early 1980s to the early 2000s in the Arctic using AVHRR data, showing increases ranging from 0.57-0.02 (Wang and Key, 2005) to 0.72 0.10 deg C per decade (Comiso, 2006). Arctic warming has implications for ice-sheet mass balance because much of the periphery of the ice sheet is near 0 deg C in the melt season and is thus vulnerable to more extensive melting (Hanna et al., 2008). The algorithm used for this work has a long history of measuring IST in the Arctic with AVHRR (Key and Haefliger, 1992). The data are currently available from 1981 to 2004 in the AVHRR Polar Pathfinder (APP) dataset (Fowler et al., 2000). J. Key1NOAA modified the AVHRR algorithm for use with MODIS (Hall et al., 2004). The MODIS algorithm is now being processed over Greenland. Issues being addressed in the production of the CDR are: time-series bias caused by cloud cover, and cross-calibration between AVHRR and MODIS instruments. Because of uncertainties, time series of satellite ISTs do not necessarily correspond with actual surface temperatures. The CDR will be validated by comparing results with in-situ (see Koenig and Hall, in press) and automatic-weather station data (e.g., Shuman et al., 2001).

Hall, Dorothy K.↗
NASA NTRS2011

Current Sheets in the Heliosheath: Voyager 1, 2009

We identified all of the current sheets for which we have relatively complete and accurate magnetic field (B) data from Voyager 1 (V1) from days of year (DOYs) 1 to 331, 2009, which were obtained deep in the heliosheath between 108.5 and 111.8 AU. Three types of current sheets were found: (1) 15 proton boundary layers (PBLs), (2) 10 and 3 magnetic holes and magnetic humps, respectively, and (3) 3 sector boundaries. The magnetic field strength changes across PBL, and the profile B(t) is linearly related to the hyperbolic tangent function, but the direction of B does not change. For each of the three sector boundaries, B rotated in a plane normal to the minimum variance direction, and the component of B along the minimum variance direction was zero within the uncertainties, indicating that the sector boundaries were tangential discontinuities. The structure of the sector boundaries was not as simple as that for PBLs. The average thickness of magnetic holes and humps (approx.30 RL) was twice that of the PBLs (approx.15 RL). The average thickness of the current sheets associated with sector boundaries was close to the thickness of the PBLs. Our observations are consistent with the hypothesis that magnetic holes and humps are solitons, which are initiated by the mirror mode instability, and evolve by nonlinear kinetic plasma processes to pressure balanced structures maintained by magnetization currents and proton drift currents in the gradients of B.

Burlaga, L. F.↗
NASA NTRS2011

Validation of a Climate-Data Record of the "Clear-Sky" Surface Temperature of the Greenland Ice Sheet

Surface temperatures on the Greenland Ice Sheet have been studied on the ground, using automatic weather station (AWS) data from the Greenland-Climate Network (GC-Net), and from analysis of satellite sensor data. Using Advanced Very High Frequency Radiometer (AVHRR) weekly surface temperature maps, warming of the surface of the Greenland Ice Sheet has been documented since 1981. We extended and refined this record using higher-resolution Moderate-Resolution Imaging Spectroradiometer (MODIS) data from March 2000 to the present. We developed a daily and monthly climate-data record (CDR) of the "clear-sky" surface temperature of the Greenland Ice Sheet using an ice-surface temperature (1ST) algorithm developed for use with MODIS data. Validation of this CDR is ongoing. MODIS Terra swath data are projected onto a polar stereographic grid at 6.25-km resolution to develop binary, gridded daily and mean-monthly 1ST maps. Each monthly map also has a color-coded image map that is available to download. Also included with the monthly maps is an accompanying map showing number of days in the month that were used to calculate the mean-monthly 1ST. This is important because no 1ST decision is made by the algorithm for cells that are considered cloudy by the internal cloud mask, so a sufficient number of days must be available to produce a mean 1ST for each grid cell. Validation of the CDR consists of several facets: 1) comparisons between ISTs and in-situ measurements; 2) comparisons between ISTs and AWS data; and 3) comparisons of ISTs with surface temperatures derived from other satellite instruments such as the Thermal Emission and Reflection Radiometer (ASTER) and Enhanced Thematic Mapper Plus (ETM+). Previous work shows that Terra MODIS ISTs are about 3 C lower than in-situ temperatures measured at Summit Camp, during the winter of 2008-09 under clear skies. In this work we begin to compare surface temperatures derived from AWS data with ISTs from the MODIS CDR.

Hall, Dorothy K.↗
NASA NTRS2011

Kinetic Simulations of Current-Sheet Formation and Reconnection at a Magnetic X Line

The integration of kinetic effects into macroscopic numerical models is currently of great interest to the plasma physics community, particularly in the context of magnetic reconnection. We are examining the formation and reconnection of current sheets in a simple, two-dimensional X-line configuration using high resolution particle-in-cell (PIC) simulations. The initial potential magnetic field is perturbed by thermal pressure introduced into the particle distribution far from the X line. The relaxation of this added stress leads to the development of a current sheet, which reconnects for imposed stress of sufficient strength. We compare the evolution and final state of our PIC simulations with magnetohydrodynamic simulations assuming both uniform and localized resistivities, and with force-free magnetic-field equilibria in which the amount of reconnect ion across the X line can be constrained to be zero (ideal evolution) or optimal (minimum final magnetic energy). We will discuss implications of our results for reconnection onset and cessation at kinetic scales in dynamically formed current sheets, such as those occurring in the terrestrial magnetotail and solar corona.

Black, C.↗
NASA NTRS2011

Current-Sheet Formation and Reconnection at a Magnetic X Line in Particle-in-Cell Simulations

The integration of kinetic effects into macroscopic numerical models is currently of great interest to the heliophysics community, particularly in the context of magnetic reconnection. Reconnection governs the large-scale energy release and topological rearrangement of magnetic fields in a wide variety of laboratory, heliophysical, and astrophysical systems. We are examining the formation and reconnection of current sheets in a simple, two-dimensional X-line configuration using high-resolution particle-in-cell (PIC) simulations. The initial minimum-energy, potential magnetic field is perturbed by excess thermal pressure introduced into the particle distribution function far from the X line. Subsequently, the relaxation of this added stress leads self-consistently to the development of a current sheet that reconnects for imposed stress of sufficient strength. We compare the time-dependent evolution and final state of our PIC simulations with macroscopic magnetohydrodynamic simulations assuming both uniform and localized electrical resistivities (C. R. DeVore et al., this meeting), as well as with force-free magnetic-field equilibria in which the amount of reconnection across the X line can be constrained to be zero (ideal evolution) or optimal (minimum final magnetic energy). We will discuss implications of our results for understanding magnetic-reconnection onset and cessation at kinetic scales in dynamically formed current sheets, such as those occurring in the solar corona and terrestrial magnetotail.

Black, C.↗
NASA NTRS2012

Face-Sheet Quality Analysis and Thermo-Physical Property Characterization of OOA and Autoclave Panels

Increased application of polymer matrix composite (PMC) materials in large vehicle structures requires consideration of non-autoclave manufacturing technology. The NASA Composites for Exploration project, and its predecessor, Lightweight Spacecraft Structures and Materials project, were tasked with the development of materials and manufacturing processes for structures that will perform in a heavy-lift-launch vehicle environment. Both autoclave and out of autoclave processable materials were considered. Large PMC structures envisioned for such a vehicle included the payload shroud and the interstage connector. In this study, composite sandwich panels representing 1/16th segments of the barrel section of the Ares V rocket fairing were prepared as 1.8 m x 2.4 m sections of the 10 m diameter arc segment. IM7/977-3 was used as the face-sheet prepreg of the autoclave processed panels and T40-800B/5320-1 for the out of autoclave panels. The core was 49.7 kilograms per square meters (3.1 pounds per cubic feet (pcf)) aluminum honeycomb. Face-sheets were fabricated by automated tape laying 153 mm wide unidirectional tape. This work details analysis of the manufactured panels where face-sheet quality was characterized by optical microscopy, cured ply thickness measurements, acid digestion, and thermal analysis.

Miller, Sandi G.↗
NASA NTRS2013

ISSM: Ice Sheet System Model

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Larour, Eric↗