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NASA NTRSDate not supplied

Roman-WFI: characterization of widefield chromatic response

Characterization of filter transmission is essential to control systematic chromatic errors in photometric surveys. Widefield surveys employ large filter optics viewed from high angles of incidence. Large optics may have variations in edge wavelength definition across their surface, and their spectral response shifts at high incidence angles. I will describe the characterization of the band definitions for the Wide Field Instrument of the Roman Space Telescope as part of its thermal vacuum test campaigns and through preparatory work. The measurement approach and analysis enable joint retrieval of chromatic response variations across the filter and focal plane. Additional tests probe out-of-band response and thermal straylight paths.

Eric Switzer↗

NASA NTRS2000

Navigation Strategy for the Mars 2001 Lander Mission

The Mars Surveyor Program (MSP) is an ongoing series of missions designed to robotically study, map and search for signs of life on the planet Mars. The MSP 2001 project will advance the effort by sending an orbiter, a lander and a rover to the red planet in the 2001 opportunity. Each vehicle will carry a science payload that will Investigate the Martian environment on both a global and on a local scale. Although this mission will not directly search for signs of life, or cache samples to be returned to Earth, it will demonstrate certain enabling technologies that will be utilized by the future Mars Sample Return missions. One technology that is needed for the Sample Return mission is the capability to place a vehicle on the surface within several kilometers of the targeted landing site. The MSP'01 Lander will take the first major step towards this type of precision landing at Mars. Significant reduction of the landed footprint will be achieved through two technology advances. The first, and most dramatic, is hypersonic aeromaneuvering; the second is improved approach navigation. As a result, the guided entry will produce in a footprint that is only tens of kilometers, which is an order of magnitude improvement over the Pathfinder and Mars Polar Lander ballistic entries. This reduction will significantly enhance scientific return by enabling the potential selection of otherwise unreachable landing sites with unique geologic interest and public appeal. A landed footprint reduction from hundreds to tens of kilometers is also a milestone on the path towards human exploration of Mars, where the desire is to place multiple vehicles within several hundred meters of the planned landing site. Hypersonic aeromaneuvering is an extension of the atmospheric flight goals of the previous landed missions, Pathfinder and Mars Polar Lander (MPL), that utilizes aerodynamic lift and an autonomous guidance algorithm while in the upper atmosphere. The onboard guidance algorithm will control the direction of the lift vector, via bank angle modulation, to keep the vehicle on the desired trajectory. While numerous autonomous guidance algorithms have been developed for use during hypersonic flight at Earth, this will be the first flight of an autonomously directed lifting entry vehicle at Mars. However, without sufficient control and knowledge of the atmospheric entry conditions, the guidance algorithm will not perform effectively. The goal of the interplanetary navigation strategy is to deliver the spacecraft to the desired entry condition with sufficient accuracy and knowledge to enable satisfactory guidance algorithm performance. Specifically, the entry flight path angle must not exceed 0.27 deg. to a 3 sigma confidence level. Entry errors will contribute directly to the size of the landed footprint and the most significant component is entry flight path angle. The size of the entry corridor is limited on the shallow side by integrated heating constraints, and on the steep side by deceleration (g-load) and terminal descent propellant. In order to meet this tight constraint it is necessary to place a targeting maneuver seven hours prior to the time of entry. At this time the trajectory knowledge will be quite accurate, and the effects of maneuver execution errors will be small. The drawback is that entry accuracy is dependent on the success of this final late maneuver. Because propulsive maneuvers are critical events, it is desirable to minimize their occurrence and provide the flight team with as much response time as possible in the event of a spacecraft fault. A mission critical maneuver at Entry - 7 hours does not provide much fault tolerance, and it is desirable to provide a strategy that minimizes reliance on this maneuver. This paper will focus on the Improvements in interplanetary navigation that will decrease entry errors and will reduce the landed footprint, even in the absence of aeromaneuvering. The easiest to take advantage of are Improvements In the knowledge of the Mars ephemeris and gravity field due to the MGS and MSP'98 missions. Improvements In data collection and reduction techniques such as "precislon ranging' and near-simultaneous tracking will also be utilized. In addition to precise trajectory control, a robust strategy for communications and flight operations must also be demonstrated. The result Is a navigation and communications strategy on approach that utilizes optimal maneuver placement to take advantage of trajectory knowledge, minimizes risk for the flight operations team, is responsive to spacecraft hardware limitations, and achieves the entry corridor. The MSP2001 mission Is managed at JPL under the auspices of the Mars Exploration Directorate. The spacecraft flight elements are built and managed by Lockheed-Martin Astronautics in Denver, Colorado.

Mase, Robert A.↗

NASA NTRS1989

Super Smooth Optics for Extra-Solar Planet Detection

The goal of imaging planets around the nearby stars has important scientific significance but requires the use of advanced methods of controlling diffracted and scattered light. Over the last three years we have undertaken a study of coronagraphic methods of controlling diffracted light and of figuring hyper-contrast optics. Progress in these two general areas have led to a proposed space-based, 1.9 meter diameter coronagraphic telescope designed specifically for very high performance in the imaging of faint objects near bright sources. This instrument, called the Circumstellar Imaging Telescope (CIT), relies on a new high efficiency coronagraph design and the careful control of scattered light by extremely smooth optics. The high efficiency coronagraph uses focal plane apodization in order to concentrate diffracted light more efficiently in the pupil. This allows convenient removal of the diffracted light by masking off parts of the telescope pupil while not sacrificing the center of the field. Reductions of diffracted light by factors exceeding 1000 are not only possible but are required in order to detect extra-solar planets. Laboratory experiments with this new design have confirmed the theoretical diffraction reductions to the limits of the optics used (factors of about 300) . The extremely high efficiency of this coronagraph puts strong constraints on the narrow angle scattered light due to figure errors in the telescope mirror. Since planets orbiting nearby stars are expected at angular distances of about 1 arcsecond, it is in this small angular range in which scattering must be controlled. The figure errors responsible for scattering in this range come from mid-spatial frequencies corresponding to correlation lengths of about 10 cm on the primary mirror. A primary mirror about 15 times smoother than the Hubble Space Telescope mirror is required for the CIT. Laboratory experiments indicate that small test mirrors can be fabricated with existing technology which come within a factor of two of this requirement.

Terrile, Richard J.↗

NASA NTRS2012

End-to-end Coronagraphic Modeling Including a Low-order Wavefront Sensor

To evaluate space-based coronagraphic techniques, end-to-end modeling is necessary to simulate realistic fields containing speckles caused by wavefront errors. Real systems will suffer from pointing errors and thermal and motioninduced mechanical stresses that introduce time-variable wavefront aberrations that can reduce the field contrast. A loworder wavefront sensor (LOWFS) is needed to measure these changes at a sufficiently high rate to maintain the contrast level during observations. We implement here a LOWFS and corresponding low-order wavefront control subsystem (LOWFCS) in end-to-end models of a space-based coronagraph. Our goal is to be able to accurately duplicate the effect of the LOWFS+LOWFCS without explicitly evaluating the end-to-end model at numerous time steps.

coronagraphs↗

NASA NTRS1980

Functional requirements for the man-vehicle systems research facility

The NASA Ames Research Center proposed a man-vehicle systems research facility to support flight simulation studies which are needed for identifying and correcting the sources of human error associated with current and future air carrier operations. The organization of research facility is reviewed and functional requirements and related priorities for the facility are recommended based on a review of potentially critical operational scenarios. Requirements are included for the experimenter's simulation control and data acquisition functions, as well as for the visual field, motion, sound, computation, crew station, and intercommunications subsystems. The related issues of functional fidelity and level of simulation are addressed, and specific criteria for quantitative assessment of various aspects of fidelity are offered. Recommendations for facility integration, checkout, and staffing are included.

Clement, W. F.↗

NASA NTRS2020

Physical Simulation Of Rocket Exhaust Aerodynamics Using Heated Ethane: Prototypical Experiments

An inaugural experimental investigation into the use of heated ethane as a motive fluid for subscale simulation of rocket exhaust plume aerodynamics has been conducted. A small, self-contained, hydrocarbon aerodynamics test stand was designed and fabricated for this purpose. Testing was performed on an aerodynamic system comprised of a 77:1 upper stage nozzle contour coupled with a passive second-throat supersonic diffuser, specifically selected for its known LOX/GH2 hot-fire performance and complex shock structure. Effects of ethane purity and stagnation temperature on the accuracy of flow field replication have been examined. All major flow features present in hot-fire tests were reproduced in heated ethane with start and unstart pressure ratio errors of approximately +4% and -5%, respectively. Steady-state test cell pressure ratio errors of ±0.5% were shown to be readily achievable when the stagnation temperature was well-controlled. Ambient-temperature nitrogen testing was also conducted for the purpose of direct comparison of the ethane method to conventional cold-flow techniques. However, its higher isentropic exponent prevented the diffuser from achieving start.

rocket↗

NASA NTRS2010

Use of Quality Controlled AIRS Temperature Soundings to Improve Forecast Skill

AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU-A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU-A are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. Also included are the clear column radiances used to derive these products which are representative of the radiances AIRS would have seen if there were no clouds in the field of view. All products also have error estimates. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20 percent, in cases with up to 90 percent effective cloud cover. The products are designed for data assimilation purposes for the improvement of numerical weather prediction, as well as for the study of climate and meteorological processes. With regard to data assimilation, one can use either the products themselves or the clear column radiances from which the products were derived. The AIRS Version 5 retrieval algorithm is now being used operationally at the Goddard DISC in the routine generation of geophysical parameters derived from AIRS/AMSU data. A major innovation in Version 5 is the ability to generate case-by-case level-by-level error estimates for retrieved quantities and clear column radiances, and the use of these error estimates for Quality Control. The temperature profile error estimates are used to determine a case-by-case characteristic pressure pbest, down to which the profile is considered acceptable for data assimilation purposes. The characteristic pressure p(sub best) is determined by comparing the case dependent error estimate (delta)T(p) to the threshold values (Delta)T(p). The AIRS Version 5 data set provides error estimates of T(p) at all levels, and also profile dependent values of pbest based on use of a Standard profile dependent threshold (Delta)T(p). These Standard thresholds were designed as a compromise between optimal use for data assimilation purposes, which requires highest accuracy (tighter Quality Control), and climate purposes, which requires more spatial coverage (looser Quality Control). Subsequent research using Version 5 sounding and error estimates showed that tighter Quality Control performs better for data assimilation proposes, while looser Quality Control better spatial coverage) performs better for climate purposes. We conducted a number of data assimilation experiments using the NASA GEOS-5 Data Assimilation System as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The model was run at a horizontal resolution of 0.5 degree latitude x 0.67 degree longitude with 72 vertical levels. These experiments were run during four different seasons, each using a different year. The AIRS temperature profiles were presented to the GEOS-5 analysis as rawinsonde profiles, and the profile error estimates (delta)T(p) were used as the uncertainty for each measurement in the data assimilation process.

Susskind, Joel↗

NASA NTRS2019

Optimization of Lyot Coronagrah focal plane masks for improved low-order wavefront sensing

The WFIRST Coronagraph uses a Low-Order Wavefront Sensing and Control (LOWFS/C) subsystem to stabilize the stellar wavefront. This is true for the Hybrid Lyot Coronagraph (HLC), the Shaped Pupil Coronagraph (SPC) spectrograph, and the SPC wide field of view modes. For the SPC spectrograph, we have found via modeling and simulations that a focal plane mask (FPM) with an elliptical phase dimple can reduce the LOWFS errors significantly compared to the conventional, circular phase dimple. For HLC designs, we concurrently optimized the FPM parameters and deformable mirror shapes using our open-source software toolbox, the Fast Linearized Coronagraph Optimizer (FALCO). This process resulted in new FPMs with non-uniform central-area phase modulation. We have found in numerical simulations that such FPMs still provide sufficient LOWFS performance. In this paper, we will present the LOWFS performance for several new HLC and SPC FPM designs.

Riggs, A.J. Eldorado↗

NASA NTRSDate not supplied

Where IMERG Goes Next: Version 08 and Beyond

With the Version 07 (V07) Integrated Multi-satellitE Retrievals for GPM (IMERG) algorithm finalized and production initiated, the focus turns to enhancements for Version 08. These include innovations not included in V07 due to time constraints, plus issues revealed by the initial V07 products. One high priority is to evaluate and revise the schemes in V07 that rectify temporal artifacts caused by the time interpolation that fills the gaps between the various passive microwave (PMW) sensor overpasses. A second priority is to improve the homogeneity between the TRMM and GPM eras by characterizing differences between the two eras, determining the causes of these differences, and applying corrections as feasible, perhaps by enforcing spatial scale consistency (an overarching issue). Certainly, we must account for GPROF and the Combined Radar-Radiometer Algorithm converting to Machine Learning schemes in V08. Other priority topics include additional automated quality control for artifacts in the IR brightness temperatures and PMW precipitation fields, revisions to the specification algorithm for the probability of liquid precipitation, and accommodating new PMW sensors, which include the next generation of small-sats. We also consider the post-V08 landscape; the final GPM reprocessing will be restricted to fixing known code or algorithmic errors. Nonetheless, there are several data sources on the horizon to consider, including more small-sat PMW radiometers, AVHRR-based precipitation estimates (most useful in high latitudes), and the ISCCP-Next Generation and GEO-Ring projects that could provide easy access to multiple geosynchronous satellite channels and enable significantly improved algorithms compared to GEO-IR alone.

George J. Huffman↗

NASA NTRS2000

Feasibility Activities Completed for the Direct Data Distribution (D(sup )3) Experiment

The Direct Data Distribution (D(sup 3)) project being designed at the NASA Glenn Research Center at Lewis Field will demonstrate a high-performance communications system that transmits information at up to 1.2 gigabits per second (Gbps) from an advanced technology payload carried by the space shuttles in low Earth orbit to small (0.9-m) autonomously tracking terminals on the Earth. The flight communications package features a solid-state, phased-array antenna operating in the commercial K-band frequency that electronically steers two independently controlled downlink beams toward low-cost tracking ground terminals. The array enables agile, vibration-free beam steering at reduced size and weight with increased reliability over traditional mechanically steered reflectors. The flight experiment will also demonstrate efficient digital modulation technology that allows transmission of substantially increased amounts of latency-tolerant data (up to 72 Gb of data per minute of contact time) with very high quality (10(exp -11) bit error rate). D(sup 3) enables transmission from low-Earth-orbit science spacecraft, the shuttles, or the International Space Station directly to NASA field centers and principle investigator sites, or directly into the commercial terrestrial telecommunications network for remote distribution and archive. The ground terminal features a cryocooled receiver for ultralow noise and a reduced antenna aperture as well as open-loop tracking for unattended operations. The D(sup 3) technology validation and service demonstration will help to facilitate NASA's transition from using Government-owned communications assets to using commercially provided services.

Wald, Lawrence W.↗

NASA NTRS1961

Study of a Solar Sensor for use in Space Vehicle Orientation Control Systems

The solar sensor described herein may be used for a variety of space operations requiring solar orientation. The use of silicon solar cells as the sensing elements provides the sensor with sufficient capability to withstand the hazards of a space environment. A method of arranging the cells in a sensor consists simply of mounting them at a large angle to the base. The use of an opaque shield placed between the cells and perpendicular to the base enhances the small-angle sensitivity while adding slightly to the bulk of the sensor. The difference in illumination of these cells as the result of an oblique incidence of the light rays from the reference source causes an electrical error signal which, when used in a battery-bridge circuit, requires a minimum of electrical processing for use in a space-vehicle orientation control system. An error which could occur after prolonged operation of the sensor is that resulting from asymmetrical aging of opposite cells. This could be periodically corrected with a balance potentiometer. A more routine error in the sensor is that produced by reflected earth radiation. This error may be eliminated over a large portion of the operation time by restricting the field of view and, consequently, the capture capability. A more sophisticated method of eliminating this error is to use separate sensors, for capture and fine pointing, along with a switching device. An experimental model has been constructed and tested to yield an output sensitivity of 1.2 millivolts per second of arc with a load resistance of 1,000 ohms and a reference light source of approximately 1,200 foot-candles delivered at the sensor.

Spencer, Paul R.↗

NASA NTRSDate not supplied

Verification of Viscous Goal-Based Anisotropic Mesh Adaptation

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics. A key ingredient for the broader acceptance of unstructured mesh adaptation is the verification of these implementations. Anisotropic metric construction methods are evaluated with analytically defined primal fields and the corresponding entropy variables as adjoint fields. This allows the comparison of different metric formulations and different implementations of the same formulation without the complications of a flow and adjoint solution method. The convergence of the output associated with the entropy variable adjoint is studied for mesh adaptation to these fields and a manufactured solution. Mesh adapted drag output is studied for two simple wings in compressible laminar flow to show fine-mesh convergence of multiple metric construction methods to less than a single drag count. The documentation of these verification exercises helps to prepare these goal-based methods for routine use in more complex simulations for production workflows.

mesh adaptation↗

NASA NTRS2009

Data Assimilation Experiments Using Quality Controlled AIRS Version 5 Temperature Soundings

The AIRS Science Team Version 5 retrieval algorithm has been finalized and is now operational at the Goddard DAAC in the processing (and reprocessing) of all AIRS data. The AIRS Science Team Version 5 retrieval algorithm contains a number of significant improvements over Version 4. Two very significant improvements are described briefly below. 1) The AIRS Science Team Radiative Transfer Algorithm (RTA) has now been upgraded to accurately account for effects of non-local thermodynamic equilibrium on the AIRS observations. This allows for use of AIRS observations in the entire 4.3 micron CO2 absorption band in the retrieval algorithm during both day and night. Following theoretical considerations, tropospheric temperature profile information is obtained almost exclusively from clear column radiances in the 4.3 micron CO2 band in the AIRS Version 5 temperature profile retrieval step. These clear column radiances are a derived product that are indicative of radiances AIRS channels would have seen if the field of view were completely clear. Clear column radiances for all channels are determined using tropospheric sounding 15 micron CO2 observations. This approach allows for the generation of accurate values of clear column radiances and T(p) under most cloud conditions. 2) Another very significant improvement in Version 5 is the ability to generate accurate case-by-case, level-by-level error estimates for the atmospheric temperature profile, as well as for channel-by-channel clear column radiances. These error estimates are used for quality control of the retrieved products. Based on error estimate thresholds, each temperature profiles is assigned a characteristic pressure, pg, down to which the profile is characterized as good for use for data assimilation purposes. We have conducted forecast impact experiments assimilating AIRS quality controlled temperature profiles using the NASA GEOS-5 data assimilation system, consisting of the NCEP GSI analysis coupled with the NASA FVGCM, at a spatial resolution of 0.5 deg by 0.5 deg. Assimilation of Quality Controlled AIRS temperature profiles down to pg resulted in significantly improved forecast skill compared to that obtained from experiments when all data used operationally by NCEP, except for AIRS data, is assimilated. These forecasts were also significantly better than to those obtained when AIRS radiances (rather than temperature profiles) are assimilated, which is the way AIRS data is used operationally by NCEP and ECMWF.

Susskind, Joel↗

NASA NTRS2018

Imaging X-Ray Polarimetry Explorer Mission Attitude Determination and Control Concept

The goal of the Imaging X-Ray Polarimetry Explorer (IXPE) Mission is to expand understanding of high-energy astrophysical processes and sources, in support of NASA's first science objective in Astrophysics: "Discover how the universe works." X-ray polarimetry is the focus of the IXPE science mission. Polarimetry uniquely probes physical anisotropies-ordered magnetic fields, aspheric matter distributions, or general relativistic coupling to black-hole spin-that are not otherwise measurable. The IXPE Observatory consists of Spacecraft and Payload modules. The Payload includes three polarization sensitive, X-ray detector units (DU), each paired with its corresponding grazing incidence mirror module assemblies (MMA). A deployable boom provides the correct separation (focal length) between the DUs and MMAs. These Payload elements are supported by the IXPE Spacecraft. A star tracker is mounted directly with the deployed Payload to minimize alignment errors between the star tracker line of sight (LoS) and Payload LoS. Stringent pointing requirements coupled with a flexible structure and a non-collocated attitude sensor-actuator configuration requires a thorough analysis of control-structure interactions. A non-minimum phase notch filter supports robust control loop stability margins. This paper summarizes the IXPE mission science objectives and Observatory concepts, and then it describes IXPE attitude determination and control implementation. IXPE LoS pointing accuracy, control loop stability, and angular momentum management are discussed.

Attitude Determination and Contro↗

NASA NTRS1990

Feasibility study of a synthesis procedure for array feeds to improve radiation performance of large distorted reflector antennas

Surface errors on parabolic reflector antennas degrade the overall performance of the antenna. Space antenna structures are difficult to build, deploy and control. They must maintain a nearly perfect parabolic shape in a harsh environment and must be lightweight. Electromagnetic compensation for surface errors in large space reflector antennas can be used to supplement mechanical compensation. Electromagnetic compensation for surface errors in large space reflector antennas has been the topic of several research studies. Most of these studies try to correct the focal plane fields of the reflector near the focal point and, hence, compensate for the distortions over the whole radiation pattern. An alternative approach to electromagnetic compensation is presented. The proposed technique uses pattern synthesis to compensate for the surface errors. The pattern synthesis approach uses a localized algorithm in which pattern corrections are directed specifically towards portions of the pattern requiring improvement. The pattern synthesis technique does not require knowledge of the reflector surface. It uses radiation pattern data to perform the compensation.

Stutzman, W. L.↗

NASA NTRS1997

Error Estimation and h-Adaptivity for Optimal Finite Element Analysis

The objective of adaptive meshing and automatic error control in finite element analysis is to eliminate the need for the application engineer from re-meshing and re-running design simulations to verify numerical accuracy. The user should only need to enter the component geometry and a coarse finite element mesh. The software will then autonomously and adaptively refine this mesh where needed, reducing the error in the fields to a user prescribed value. The ideal end result of the simulation is a measurable quantity (e.g. scattered field, input impedance), calculated to a prescribed error, in less time and less machine memory than if the user applied typical uniform mesh refinement by hand. It would also allow for the simulation of larger objects since an optimal mesh is created.

Cwik, Tom↗

NASA NTRS1986

Application of a low order panel method to complex three-dimensional internal flow problems

An evaluation of the ability of a low order panel method to predict complex three-dimensional internal flow fields was made. The computer code VSAERO was used as a basis for the evaluation. Guidelines for modeling internal flow geometries were determined and the effects of varying the boundary conditions and the use of numerical approximations on the solutions accuracy were studied. Several test cases were run and the results were compared with theoretical or experimental results. Modeling an internal flow geometry as a closed box with normal velocities specified on an inlet and exit face provided accurate results and gave the user control over the boundary conditions. The values of the boundary conditions greatly influenced the amount of leakage an internal flow geometry suffered and could be adjusted to eliminate leakage. The use of the far-field approximation to reduce computation time influenced the accuracy of a solution and was coupled with the values of the boundary conditions needed to eliminate leakage. The error induced in the influence coefficients by using the far-field approximation was found to be dependent on the type of influence coefficient, the far-field radius, and the aspect ratio of the panels.

Ashby, D. L.↗

NASA NTRS2015

Reconfigurable Very Long Instruction Word (VLIW) Processor

Future NASA missions will depend on radiation-hardened, power-efficient processing systems-on-a-chip (SOCs) that consist of a range of processor cores custom tailored for space applications. Aries Design Automation, LLC, has developed a processing SOC that is optimized for software-defined radio (SDR) uses. The innovation implements the Institute of Electrical and Electronics Engineers (IEEE) RazorII voltage management technique, a microarchitectural mechanism that allows processor cores to self-monitor, self-analyze, and selfheal after timing errors, regardless of their cause (e.g., radiation; chip aging; variations in the voltage, frequency, temperature, or manufacturing process). This highly automated SOC can also execute legacy PowerPC 750 binary code instruction set architecture (ISA), which is used in the flight-control computers of many previous NASA space missions. In developing this innovation, Aries Design Automation has made significant contributions to the fields of formal verification of complex pipelined microprocessors and Boolean satisfiability (SAT) and has developed highly efficient electronic design automation tools that hold promise for future developments.

Velev, Miroslav N.↗