Abstract: A graphical user interface includes GUI elements configured for defining discretized base geometry data for a model of a physical system, receiving a first input representing a user instruction to add a perfectly matched layer to the model, receiving a second input representing the user selection of boundaries that define a base geometry, and receiving a third input representing extra geometry meshing instructions. Extra geometry line segment data is discretized representing an outward direction of a PML from the boundary according to the extra geometry meshing instructions. Weak form expressions representing a wave-related phenomena are formed based on received PML settings and physics settings parameterized using discretized base geometry data and discretized extra geometry data. Matrix data are generated based on the formed weak form expressions. A solution to a simulation of the wave-related phenomena of the model is generated based on the formed weak form expressions.

Abstract: Systems and methods for modeling physical systems include displaying geometric representation of a physical system on a physics simulation system. User-selection inputs received indicate, for mesh elements, selections of dependent variable shape function spaces representing dependent variables. Geometry shape function space options for simulating the physical system are determined that are common to mesh elements and include a serendipity shape function space of second order or higher. A determined geometry shape function space option is a subset of a combination of the dependent variable shape function spaces and satisfies accuracy criteria based on an accuracy ordering of shape function spaces. A finite element mesh for the physical system is created based on the mesh elements, a selected geometry shape function space, and the selection of dependent variable shape function spaces.

Abstract: A simulation apparatus for adding extra geometries to a model of a physical system. The apparatus is configured to modify a geometry of a model of a physical system represented in terms of a combined set of equations. Instructions on the apparatus cause one or more processors to perform, upon execution, acts comprising: (i) receiving a base geometry of the physical system, (ii) receiving one or more extra geometries associated with the base geometry, (iii) determining first geometric entities of the base geometry and second geometric entities of the extra geometry, (iv) adding the extra geometries to the base geometry by computing a product geometry of the determined first geometric entities and the second geometric entities, (v) generating an updated combined set of equations including representations of the product geometry, and (vi) generating a graphical representation of the product geometry, the graphical representation configured for display on the display device.

Abstract: A simulation apparatus for adding extra geometries to a model of a physical system. The apparatus is configured to modify a geometry of a model of a physical system represented in terms of a combined set of equations. Instructions on the apparatus cause one or more processors to perform, upon execution, acts comprising: (i) receiving a base geometry of the physical system, (ii) receiving one or more extra geometries associated with the base geometry, (iii) determining first geometric entities of the base geometry and second geometric entities of the extra geometry, (iv) adding the extra geometries to the base geometry by computing a product geometry of the determined first geometric entities and the second geometric entities, (v) generating an updated combined set of equations including representations of the product geometry, and (vi) generating a graphical representation of the product geometry, the graphical representation configured for display on the display device.

Abstract: A simulation apparatus for adding extra geometries to a model of a physical system. The apparatus is configured to modify a geometry of a model of a physical system represented in terms of a combined set of equations. Instructions on the apparatus cause one or more processors to perform, upon execution, acts comprising: (i) receiving a base geometry of the physical system, (ii) receiving one or more extra geometries associated with the base geometry, (iii) determining first geometric entities of the base geometry and second geometric entities of the extra geometry, (iv) adding the extra geometries to the base geometry by computing a product geometry of the determined first geometric entities and the second geometric entities, (v) generating an updated combined set of equations including representations of the product geometry, and (vi) generating a graphical representation of the product geometry, the graphical representation configured for display on the display device.

Abstract: The present invention relates to a solution for solving an ill-posed inverse problem in image analysis, e.g. in an electron tomography application in order to recover a structure of a sample. The solution is provided for instance as a method comprising steps of determining reliable prior knowledge about the solution, determining initial guess for the solution and determining the corresponding forward operator, deciding upon model of stochasticity, deciding on suitable regularization method, deciding on updating scheme, and producing a sequence using the set configuration.

Abstract: The present invention relates to a solution for solving an ill-posed inverse problem in image analysis, e.g. in an electron tomography application in order to recover a structure of a sample. The solution is provided for instance as a method comprising steps of determining reliable prior knowledge about the solution, determining initial guess for the solution and determining the corresponding forward operator, deciding upon model of stochasticity, deciding on suitable regularization method, deciding on updating scheme, and producing a sequence using the set configuration.