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US 8,510,091 B1Granted
Domain decomposition formulations for simulating electromagnetic fields
AssigneeSAS IP, LLC
InventorsKezhong Zhao, Din-Kow Sun
Life of this patent
Estimating the term…
Abstract
Disclosed are domain-decomposition approaches to simulations of electromagnetic fields may that, in various embodiments, use second-order Robin transmission conditions at subdomain boundaries.
Claims21
A computer-implemented method for simulating physical properties of an electromagnetic field in a user-defined domain, the method comprising:
- storing a user-defined domain in a memory;
- decomposing, with a processor, the user-defined domain into a plurality of subdomains;
- modeling the electromagnetic field within the plurality of subdomains, using higher-order Robin transmission conditions at interfaces between the subdomains;
- and
- computationally simulating the physical properties of the electromagnetic field in the domain based on the model,
- wherein the higher-order Robin transmission conditions comprise Robin coefficients that cause the simulated electromagnetic field to converge faster than a simulation based solely on first-order Robin conditions;
- and
- wherein the Robin coefficients are selected based on, at least in part:
- (i) a basis order of finite elements defined over a mesh grid of at least one subdomain, and (ii) constants related to two smallest side lengths of a bounding box of the user-defined domain.
6 more elements
A computer-implemented method for simulating physical properties of an electromagnetic field in a user-defined domain, the method comprising:
- storing a user-defined domain in a memory;
- decomposing, with a processor, the user-defined domain into a plurality of subdomains;
- modeling the electromagnetic field within the plurality of subdomains;
- based on the model, generating a block system matrix whose diagonal blocks correspond to the subdomains, each diagonal block having block lower triangular form;
- and
- based at least in part on the block system matrix, computationally simulating the physical properties of the electromagnetic field
- wherein generating the block system matrix comprises using Robin transmission conditions comprising Robin coefficients,
- wherein the Robin coefficients are selected based on, at least in part, constants related to two smallest side lengths of a bounding box of the user-defined domain.
5 more elements
A computer system for simulating physical properties of an electromagnetic field in a user-defined domain, the system comprising:
- a computer containing
- (a) a memory for storing parameters representative of the electromagnetic field and the user- defined domain;
- and
- (b) an analysis module for:
- decomposing the user-defined domain into a plurality of subdomains;
- modeling the electromagnetic field within the plurality of subdomains, using higher-order Robin transmission conditions at interfaces between the subdomains;
- and
- (c) a simulation module for simulating the physical properties of the electromagnetic field based at least in part on the block system matrix,
- wherein the higher-order Robin transmission conditions comprise Robin coefficients that cause the simulated electromagnetic field to converge faster than a simulation based solely on first-order Robin conditions, and
- wherein the Robin coefficients are selected based on, at least in part:
- (i) a basis order of finite elements defined over a mesh grid of at least one subdomains, and (ii) constants related to two smallest side lengths of a bounding box of the user-defined domain.
8 more elements
A computer system for simulating physical properties of an electromagnetic field in a user-defined domain, the system comprising:
- a computer containing
- (a) a memory for storing parameters representative of the electromagnetic field and the user-defined domain;
- and
- (b) an analysis module for:
- decomposing the user-defined domain into a plurality of subdomains;
- modeling the electromagnetic field within the plurality of subdomains;
- generating, based on the model, a block system matrix system matrix whose diagonal blocks correspond to the subdomains, each diagonal block having block lower triangular form;
- and
- (c) a simulation module for simulating the physical properties of the electromagnetic field based at least in part on the block system matrix,
- wherein generating the block system matrix comprises using Robin transmission conditions comprising Robin coefficients,
- wherein the Robin coefficients are selected based on, at least in part, constants related to two smallest side lengths of a bounding box of the user-defined domain.
8 more elements
Dependencies are inferred from the claim text.