Moment-Based Representation for Interoperable Analysis

A system for computing integrals over geometric domains, the system comprising:

• a first computing device comprising a first computational analysis system for carrying out operations including calculation of moment-vectors for arbitrary geometric representations and arbitrary field representations of objects;
• and
• a second computing device comprising a second computational analysis system for carrying out operations including analysis of physical and/or operational characteristics of simulated objects,
• wherein the first computational analysis system is configured to:
• receive data comprising a geometric representation of an object and a field representation of the object, the geometric representation specifying a geometric domain corresponding to a shape and a contained spatial region of the object, and the field representation specifying a spatially varying physical quantity within the geometric domain;
• computationally integrate a predetermined set of basis functions over the geometric domain multiplied by respective field values at integration points to derive a moment-vector for the object, the moment-vector encapsulating an analytic formulation of the geometric domain and an associated field that is independent of the geometric representation of the object and the field representation of the object;
• computationally generate quadrature rules for integrating an arbitrary function by applying moment-fitting to the moment-vector, wherein the quadrature rules incorporate quadrature weights that account for the associated field;
• and
• provide the quadrature rules to the second computational analysis system via a common interface for transfer of quadrature rules between the first and second computational analysis systems;
• and wherein the second computational analysis system is configured to:
• independently of the geometric representation and the field representation of the object, computationally integrate the arbitrary function over the geometric domain by applying the quadrature rules.

A first-stage computing device comprising:

• one or more processors;
• memory,
• and instructions stored in the memory that, when executed by the one or more processors, cause the first-stage computing device to carry out operations including:
• receiving data comprising a geometric representation and a field representation of an object, the geometric representation specifying a geometric domain corresponding to a shape and a contained spatial region of the object, and the field representation specifying a spatially varying physical quantity within the geometric domain;
• computationally integrating a predetermined set of basis functions over the geometric domain multiplied by respective field values at integration points to derive a moment-vector for the object, the moment-vector encapsulating an analytic formulation of the geometric domain that is independent of the geometric representation of the object and the field representation of the object;
• computationally generating quadrature rules for integrating an arbitrary function by applying moment-fitting to the moment-vector, wherein the quadrature rules incorporate quadrature weights that account for the associated field;
• and
• providing the moment-vector to a second-stage computing device;
• wherein the second-stage computing device is configured to:
• independently of the geometric representation of the object and the field representation of the object, computationally integrate the arbitrary function over the geometric domain by applying the quadrature rules.

A second-stage computing device comprising:

• one or more processors;
• memory,
• and instructions stored in the memory that, when executed by the one or more processors, cause the second-stage computing device to carry out operations including:
• receiving, from a first-stage computing device, quadrature rules for integrating an arbitrary function multiplied by a field representation of an object over a geometric domain corresponding to a shape and a contained spatial region of the object, wherein the geometric domain is specified according to a geometric representation of the object and the field representation comprises a material field expressed analytically as a tensor field specifying a spatially varying physical quantity within the geometric domain;
• and
• independently of the geometric representation and the field representation of the object, computationally integrating the arbitrary function over the geometric domain by applying the quadrature rules;
• wherein the quadrature rules are computed by the first-stage computing device, the first-stage computing device being configured to:
• receive data comprising the geometric representation and the field representation of the object;
• computationally integrate a predetermined set of basis functions over the geometric domain multiplied by respective field values at integration points to derive the moment-vector for the object, the moment-vector encapsulating an analytic formulation of the geometric domain that is independent of the geometric representation of the object and the field representation of the object;
• computationally generate the quadrature rules for integrating the arbitrary function by applying moment-fitting to the moment-vector, wherein the quadrature rules incorporate quadrature weights that account for the associated field;
• and
• provide the moment-vector to the second-stage computing device.

A non-transitory computer-readable medium having instructions stored thereon that, when executed by the one or more processors of a system for computing integrals over geometric domains, cause the system to carry out operations including:

• receiving, at a first computing device, data comprising a geometric representation and a field representation of an object of an object, the geometric representation defining a geometric domain descriptive of a shape and a contained spatial region of the object, and the field representation specifying a spatially varying physical quantity within the geometric domain;
• at the first computing device, computationally integrating a predetermined set of basis functions over the geometric domain multiplied by respective field values at integration points to derive a moment-vector for the object, the moment-vector encapsulating an analytic description of the geometric domain and an associated field that is independent of the geometric representation of the object and the field representation of the object;
• at the computing device, computationally generating quadrature rules for integrating an arbitrary function by applying moment-fitting to the moment-vector, wherein the quadrature rules incorporate quadrature weights that account for the associated field;
• providing the quadrature rules to a second computing device;
• and
• at the second computing device, independently of the geometric representation and the field representation of the object, computationally integrating the arbitrary function over the geometric domain by applying the quadrature rules.