Pasadena, CA, United States

Mathematical Systems & Solutions, Inc.

www.mathsys.net
Pasadena, CA, United States

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Grant
Agency: Department of Defense | Branch: Air Force | Program: STTR | Phase: Phase I | Award Amount: 99.90K | Year: 2010

We propose algorithm development and efficient GPU implementation of numerical PDE solvers based on four novel high-order methodologies: 1) High-order Discontinuous Galerkin approaches, 2) Fast High-Order boundary integral methods, 3) Convergent FFT-based methodologies for evaluation of computational boundary conditions, and 4) Fourier Continuation methods. These methodologies are applicable to a vast array of problems of critical interest to the Air Force, encompassing computational electromagnetics and computational acoustics (including the convective wave equation), isotropic and anisotropic elasticity, heat transfer and fluid-dynamics (including gas-dynamics, incompressible hydrodynamics, shock-dynamics and slow viscous flow). Parallel CPU implementations of such solvers have provided some of the most efficient PDE solution methods in existence today: in some cases, our algorithms are up to one-thousand times faster than the best alternative solvers. We have further demonstrated that GPU implementations of DG solvers can outperform corresponding CPU implementations, in comparably priced multi-core CPUs, by factors of fifty. The proposed effort thus seeks to combine the power of two game-changing emerging paradigms: fast high-order PDE solvers and many-core/GPU computer architectures. We believe the resulting methodologies will significantly advance the state of the art in computational science, and will play central roles in science and engineering in years to come. BENEFIT: The PDE software needs of large high-tech companies, government labs and DoD (such as Lockheed Martin, Northrop Grumman, NASA, DoD agencies, etc.) are massive. MathSys Inc. is well positioned to cater to the needs of such entities, and has open ties at key levels of such organizations. We are certain that the successful completion of the proposed development effort will find manifold uses and it will generate significant business opportunities for our company.


Grant
Agency: Department of Defense | Branch: Air Force | Program: STTR | Phase: Phase I | Award Amount: 149.96K | Year: 2013

ABSTRACT: We propose development of an efficient physics-based computational capability for real-time radar location of targets in cluttered environments. Our effort will focus, in particular, on air traffic targets in static natural environments that include dynamic effects such as spinning wind turbines. The proposed methodology models radar signal scattering in cluttered environments on the basis of the time-dependent Maxwell's equations formulated, in a single computational methodology, in terms of 1) Moving- and fixed-domain overlapping computational meshes, as well as 2) The dispersionless Fourier-Continuation method, and 3) A novel methodology for evaluation of computational boundary conditions and long-range propagation at essentially zero cost. BENEFIT: Our effort seeks to provide a software solution for users of simulation tools for which the limitations implicit in existing solvers represent a significant handicap. These include the military, (Navy, Air Force, and Army) as well as commercial concerns (air-framers, space research agencies, remote sensing and medical imaging developers, etc). Thus, there is a significant market for the proposed improved innovative solutions in high-tech industry, and in pursuing the present project MathSys Inc. seeks to cater to that need. Our connections with DoD and industrial scientists, as described below, form the basis of our overall commercialization strategy.


Grant
Agency: Department of Defense | Branch: Air Force | Program: STTR | Phase: Phase II | Award Amount: 749.96K | Year: 2012

ABSTRACT: This effort focuses on development of efficient algorithms for the simulation of propagation and scattering of electromagnetic fields within and around structures that (i) Consist of complex combinations of penetrable materials as well as perfect and imperfect conductors, and, (ii) Possess complex geometrical characteristics, including open surfaces and metallic coatings, as well as geometric singularities: corners, edges and multi-scale featuresincluding geometries that contain simultaneously structures at length-scales at the level of electronics and complete aircraft. These are configurations of fundamental importance in diverse fields, with application to (a) Electromagnetic compatibility (EMC), (b) Electromagnetic interference on cavity-bound electronics (EMI), (c) Evaluation of electromagnetic response of dielectric/magnetic coated conductors, and (d) Evaluation of scattering by modern metallic/nonmetallic aircraft structuresamongst many others. The simulation of electromagnetic wave propagation in such complex structures gives rise to a host of significant computational challenges; these issues will be addressed through application of MathSys'innovative integral equation methodologies, with hardware implementations in both classical serial processors and large parallel infrastructures. In view of recent the Phase I work and other recent efforts, we submit the proposed consonant use of accurate and efficient mathematical algorithms and state-of-the-art numerical implementations will enable solution of previously intractable problems. BENEFIT: The PDE software needs of large high-tech companies, government labs and DoD (such as Lockheed Martin, Northrop Grumman, NASA, DoD agencies, etc.) are massive. MathSys Inc. is well positioned to cater to the needs of such entities, and has open ties at key levels of such organizations. We are certain that the successful completion of the proposed development effort will find manifold uses and it will generate significant business opportunities for our company.


Grant
Agency: Department of Defense | Branch: Air Force | Program: STTR | Phase: Phase II | Award Amount: 749.98K | Year: 2014

ABSTRACT: We propose development of an efficient physics-based computational capability for simulation of complex MIMO radar clutter, with applicability to single- and multi-platform transmit-receive systems, which accounts accurately, on the basis of Maxwell's equations, for all relevant multi-path propagation and scattering effects. Our effort will enable simulation of scattering by realistic environmental clutter sources (arising from topography, vegetation, urban areas, etc.), for arbitrarily prescribed waveforms (thus enabling applicability to general radar systems), while accounting for multiple-scattering, complex targets (vehicles, missiles, etc.) and Doppler effects. The proposed work will thus enable, for the first time, simulation and optimization of the detection properties of MIMO radars in general configurations of vehicles and clutter scenes. BENEFIT: Our effort seeks to provide a software solution for users of simulation tools for which the limitations implicit in existing solvers represent a significant handicap. These include the military, (Navy, Air Force, and Army) as well as commercial concerns (air-framers, space research agencies, remote sensing and medical imaging developers, etc). Thus, there is a significant market for the proposed improved innovative solutions in high-tech industry, and in pursuing the present project MathSys Inc. seeks to cater to that need. Our connections with DoD and industrial scientists, as described below, form the basis of our overall commercialization strategy.


Grant
Agency: Department of Defense | Branch: Navy | Program: SBIR | Phase: Phase II | Award Amount: 437.45K | Year: 2013

We propose development of a software capability which, based on use of accurate and efficient exact-physics computational electromagnetics (CEM) solvers together with a combination of automated and interactive optimization tools, will enable optimization of the properties of on-platform mounted-antenna systems. For accuracy and modeling flexibility the proposed codes are based on the fast, high-order frequency-domain algorithms put forth recently by our team-which can accurately and efficiently resolve both low- and high-frequency behavior while accounting for scattering, transmission and absorption by metallic, dielectric and magnetic components. These solvers have provided some of the most efficient PDE solution methods in existence: they can successfully tackle electrically large problems in complex engineering geometries, including problems which are significantly beyond the capabilities of the most competitive alternative solvers. Our novel parallel CPU implementations of these algorithms, in turn, demonstrate a high degree of parallel efficiency. Our overall approach to in-situ antenna optimization, finally, relies on a combination of classical gradient-based optimization methods together with a new technique based on use of"low-rank electromagnetic bases", which can yield a large number of scattering solutions (and thus, enable efficient optimization algorithms) from a limited number of actual solution runs.


Grant
Agency: Department of Defense | Branch: Navy | Program: SBIR | Phase: Phase I | Award Amount: 149.46K | Year: 2012

We propose development of a software package which, based on use of accurate and efficient exact-physics computational electromagnetics (CEM) solvers together with a combination of automated and interactive optimization tools, will enable optimization of the properties of on-platform mounted-antenna systemsand, when possible, recovery of original free-space antenna characteristics. For accuracy and modeling flexibility the proposed codes combine the fast, high-order frequency- and time-domain algorithms put recently by our teamwhich can accurately and efficiently resolve both low- and high-frequency behavior while accounting for scattering, transmission and absorption by metallic, dielectric and magnetic components. These solvers have provided some of the most efficient PDE solution methods in existence: in some cases, our algorithms are up to one-thousand times faster, for a given accuracy, than some of the best alternative solvers. Our overall approach to in-situ antenna optimization, in turn, relies on a combination of classical gradient-based optimization methods (applied to parameters defining geometrical shapes) and a new"path-following"technique, in which optimal antenna shapes and mountings are produced incrementally, as secondary structures (gimbal, secondary antennae, airframe, radome, electronics, etc) are subsequently introduced.


Grant
Agency: Department of Defense | Branch: Missile Defense Agency | Program: SBIR | Phase: Phase I | Award Amount: 99.69K | Year: 2012

We propose development of accurate and efficient exact-physics computational electromagnetics (CEM) solvers for accurate evaluation of RF signature characteristics of complex targets of interest to MDA. For accuracy and modeling flexibility the proposed codes combine novel fast, high-order frequency- and time-domain algorithms put forth in recent yearswhich can accurately and efficiently resolve both low- and high-frequency behavior while accounting for scattering, transmission and absorption. These solvers have provided some of the most efficient PDE solution methods in existence: in some cases, our algorithms are up to one-thousand times faster, for a given accuracy, than some of the best alternative solvers. Our novel parallel CPU and GPU implementations of these algorithms, in turn, demonstrate a high degree of efficiency, and, in particular: perfect parallel efficiency for the time-domain algorithms, 50%-to-70% parallel efficiency for integral equation algorithms, and nearly optimal GPU speedups, by a factors as high as 90, from the corresponding CPU implementations (for single Tesla C1060 GPU). Existing partnerships with relevant industries will help secure a significant customer base for the forthcoming software products. In all, our company is favorably positioned to deliver a powerful software tool for analysis of RF missile signatures as described in Topic MDA11-039.


Grant
Agency: Department of Defense | Branch: Air Force | Program: STTR | Phase: Phase I | Award Amount: 99.61K | Year: 2012

ABSTRACT: We propose development of an efficient physics-based computational capability for simulation of complex MIMO-radar clutter, with applicability to single- and multi-platform transmitter-receiver systems, which accounts accurately, on the basis of Maxwell's equations, for all relevant multi-path propagation and scattering effects. Our effort will enable simulation of scattering by realistic environmental clutter sources (arising from topography, vegetation, urban areas, etc.), for arbitrarily prescribed waveforms (thus enabling optimization of the detection performance of MIMO radars), while accounting for multiple-scattering from carriers (aircraft or other vehicles), complex targets (vehicles, missiles, etc.) and Doppler effects. BENEFIT: Our effort seeks to provide a software solution for users of simulation tools for which the limitations implicit in existing solvers represent a significant handicap. These include the military, (Navy, Air Force, and Army) as well as commercial concerns (air-framers, space research agencies, remote sensing and medical imaging developers, etc). Thus, there is a significant market for the proposed improved innovative solutions in high-tech industry, and in pursuing the present project MathSys Inc. seeks to cater to that need. Our connections with DoD and industrial scientists, as described below, form the basis of our overall commercialization strategy.


Grant
Agency: Department of Defense | Branch: Navy | Program: STTR | Phase: Phase I | Award Amount: 79.98K | Year: 2015

We propose development of a software capability which, based on use of MathSysaccurate and efficient exact-physics computational electromagnetics (CEM) solvers, will enable modeling and optimization of the properties of on-platform pRFID tag/reader antenna systems. Passive Radio Frequency Identification devices (pRFID) mounted on complex rotorcrafts pose challenging modeling problems: since pRFID power outputs are often at least three orders of magnitude below the reader's signal power, modeling of such setups requires use of solvers that can produce numerical solutions with several digits of accuracy. And, for RFID operating at frequencies at of 2.5 GHz or higher, for example, the electrical size of the platform on which the RFID tag-reader system is mounted can be hundreds of wavelengths in size. Such modeling requirements and constraints exceed the capabilities of all currently available software modeling and simulation tools. While computationally inexpensive, ray-tracing based methods can, at best, serve as an ``informed guess'' and are unable to provide sufficient accuracy in complex multipath scattering environments. The proposed extension of MathSys solvers will enable effective simulation the highly challenging pRFID-in-rotorcraft configurations throughout the relevant range of the electromagnetic spectrum.


Grant
Agency: Department of Defense | Branch: Navy | Program: SBIR | Phase: Phase I | Award Amount: 79.99K | Year: 2015

We propose development of a software capability which, based on use of accurate and efficient exact-physics computational electromagnetics (CEM) solvers together with a CAD-import (Computer Aided Design) and direct CAD-to-EM capabilities, will enable modeling and simulation of properties of on-platform mounted-antenna systems for platforms one-thousand wavelengths in size and beyond. For accuracy and modeling flexibility the proposed codes are based on MathSys fast, high-order frequency-domain algorithms together with a number of highly significant proposed innovations. The resulting solvers will be able to accurately and efficiently simulate generation, propagation and scattering of waves within and around complex scattering structures of very large electrical sizeswhile accounting in a physically exact manner for scattering, transmission and absorption by complex metallic, dielectric and magnetic structures.

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