KR101828020B1 - System and Method for processing Grid Data on the Cubed Sphere using Spectral Element High Order Digital Filter - Google Patents

Abstract

The present invention relates to an apparatus and method for processing hexahedral spherical aberration data by using a spectral element method digital filter which constitutes a local area higher order filter using a hexahedral spherical spectroscopic element method and increases computational efficiency and stability, GLLIP constructs GLLIP (Gauss-Lobatto-Lagrange Interpolating Polynomial), which is a basis function for discretization using the spectral element method; GLLIP is used to develop a Laplacian operator and integrate it on one element An operator matrix building unit for obtaining a discrete Laplacian operator matrix for each element N _l x N _l regional area setting unit combines the elements of the Laplacian matrix of the local area; discrete Laplacian for the local area; operator matrix combination unit for combining the discrete Laplacian operator matrix in accordance with the engagement element region is defined for each element And a filter matrix building unit for substituting the filter matrix into a filter equation using the operator matrix and constructing a discrete filter matrix operator matrix.

Description

[TECHNICAL FIELD] The present invention relates to an apparatus and a method for processing a hexahedral spherical lattice data using a digital filter,

The present invention relates to a spectral element digital filter, and more particularly, to an apparatus and method for processing a hexahedral spherical lattice data using a spectral element method digital filter having a high-order domain filter using a hexahedral spherical spectral element method and improving the efficiency and stability of calculation .

A numerical weather prediction model is a mathematical model for calculating the atmospheric and oceanic dynamical equations, physical parametric equations, etc. to predict future weather from current or past diurnal conditions.

The dynamic core part, which is an important component of the numerical weather forecast model, describes physical quantities such as wind, temperature, air pressure, humidity and entropy in the atmosphere as a governing equation including a plurality of partial differential equations, It is the part that solves numerically the solution of.

For the numerical calculation of the mechanical core portion, a calculation method for numerical solution of the partial differential equation is required together with the positional information of the variables constituting the governing equation. The positional information of the variables can be obtained from any spherical grid coordinate system for indicating the horizontal, vertical position on the earth.

For example, a horizontal coordinate system of normal latitude and longitude may be used to indicate the horizontal position of the variables. In addition, a vertical coordinate system such as a barometric altitude, sea level altitude, etc. may be used to indicate the vertical position of the variables.

On the other hand, a spectral element method can be used as a calculation method for numerical solution of the partial differential equation.

The spectral element method calculates a numerical solution of a partial differential equation by dividing the entire computational space by element and developing a Legendre polynomial or a Lagrange polynomial in each element Method.

Recently, techniques for calculating numerical solutions using a cubed-sphere grid have been developed in order to solve the deviation of the lattice distribution of the polar regions and the equatorial regions of the horizontal coordinate system of latitude and longitude.

When a spectral element method is applied to a hexahedral sphere, it is possible to perform intra-element calculation and communication between elements for a plurality of elements by using a message passing interface (MPI) calculation-communication method.

Recently, many numerical models using the hexahedral spherical spectroscopic element method have been developed. Accordingly, a technique for removing the noise of the hexahedral spherical spectroscopic element model or the lattice data is required.

An explicit noise cancellation method using a hexahedral spectral element method is widely used but is sometimes inaccurate and unstable. Particularly, in high-order filtering, the degree becomes very serious.

Therefore, it is required to develop a new technique to improve the quality of lattice data and numerical forecast data by processing the data on the hexagonal lattice grid with high-speed separation and noise.

Korean Patent Publication No. 10-2015-0053017 Korean Patent No. 10-1491022 Korean Patent Publication No. 10-2015-0053018

The present invention solves the problem of the conventional digital filter of the spectroscopic element method. The present invention is to solve the problem of the conventional digital filter of the spectroscopic element method by using a spectral element method digital filter which constitutes a local domain higher order filter using a hexahedral spherical spectroscopic element method, And an object of the present invention is to provide an apparatus and a method for processing.

An object of the present invention is to provide an apparatus and method for processing hexahedral spherical aberration data using a spectroscopic element method digital filter capable of performing stable and accurate filtering by introducing an implicit noise cancellation method using a hexahedral spherical spectroscopic element method .

The present invention relates to a device for processing hexahedral sphere lattice data using a spectral element method digital filter capable of performing filtering with higher calculation efficiency than an implicit noise elimination method for a bulb area by using an implicit noise elimination method for a local area The purpose of the method is to provide.

The present invention relates to a spectral element method using a spectral element method digital filter which can improve the efficiency and stability of a calculation by constructing a local area higher order filter using a hexahedral spherical spectroscopic element method and efficiently apply it to a numerical model of hexahedral spherical lattice data and a hexahedral spherical spectroscopic element And to provide a device and method for processing cube spherical lattice data.

The present invention relates to a method and apparatus for processing hexahedral sphere data using a spectroscopic element digital filter that improves the quality of lattice data and numerical forecast data by processing the data on the hexahedral sphere grid at high speeds And an object of the present invention is to provide an apparatus and method.

The present invention relates to a device and a method for processing hexahedral spherical aberration data using a spectral element method digital filter that ensures high parallel scalability and isotropic filtering of high resolution hexahedral spherical aberration data by using a hexahedral spherical spectroscopic element method The purpose is to provide.

The objects of the present invention are not limited to the above-mentioned objects, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.

In order to achieve the above object, a device for processing a hexahedral spherical lattice data using a spectral element method digital filter according to the present invention includes a hexahedral spherical lattice constituting a hexagonal spherical lattice, (Gauss-Lobatto-Lagrange Interpolating Polynomial ) configuration GLLIP configuration unit; using GLLIP, part deploy the Laplacian operator, and by integrating them for the element construction, each element by the operator to obtain a discrete Laplacian operator matrix matrix; N _l x N _l regional area setting unit combines the elements of the Laplacian matrix of the local area; discrete Laplacian for the local area; operator matrix combination unit for combining the discrete Laplacian operator matrix in accordance with the engagement element region is defined for each element And a filter matrix building unit for substituting the filter matrix into a filter equation using the operator matrix and constructing a discrete filter matrix operator matrix.

Here, the hexahedral sphere lattice configuration unit is configured such that the user specifies the number of elements and lattice points, divides each surface of the hexahedral sphere into a finite number of elements, and a lattice point is defined in each element .

And an inverse matrix computation unit for inversely preliminarily inverting the discrete filter matrix operator constructed for each element and using it in calculation.

In the area area setting unit, the number of coupling elements N _l is given by FLOOR [6 ^-1 N _e + N ^-1 ], where FLOOR is a floor function.

In order to accomplish the other object, a method for processing a hexahedral spherical grating data using a spectroscopic element digital filter according to the present invention comprises the steps of constructing a hexahedral spherical grating, using a Gauss-Lobatto- Interpolating Lagrange Polynomial) configuration GLLIP configuration method comprising; using GLLIP, deploy the Laplacian operator, and building this by the integral element for the operator to get the respective components by the discrete Laplacian operator matrix, the matrix phase; N _l x A local region setting step of constructing a Laplacian matrix for a local region by combining N _l elements, an operator matrix combining unit for combining discrete Laplacian operator matrices along a join element region defined for each element, a discrete Laplacian And constructing a discrete filter matrix operator matrix by substituting the filter matrix into a filter equation using an operator matrix.

Here, the method further includes a inverse matrix calculation step of inverting the discrete filter matrix operator constructed for each element in advance and using the discrete filter matrix operator for calculation.

The apparatus and method for processing hexahedral spherical aberration data using the spectral element method digital filter according to the present invention have the following effects.

First, the efficiency and stability of computation can be improved by constructing a local domain higher order filter using the hexahedral spherical spectroscopic element method.

Second, it introduces an implicit noise removal method using hexahedral spectral element method, so that stable and accurate filtering can be performed.

Third, the implicit noise cancellation method for the local area can be used to perform the filtering with higher calculation efficiency than the implicit noise cancellation method for the bulb area.

Fourth, by constructing a high - order domain filter using the hexahedral spectral element method, the efficiency and stability of computation are improved, and it is applied to the hexahedral spherical grid data and the hexahedral spherical element numerical model efficiently.

Fifth, it is possible to improve the quality of lattice data and numerical forecast data by processing the data on the hexagonal lattice with high-speed separation and noise according to the scale.

Sixth, the parallel scalability is ensured by using the hexahedral spherical spectroscopic element method, and the isotropic filtering of the high-resolution hexahedral spherical aberration data can be applied, so that it can be applied to various fields such as fluid dynamics and earth science using the spectroscopic element method Do.

1 is a block diagram of a device for processing hexahedral spherical aberration data using a spectroscopic element digital filter according to the present invention
2 is a flowchart illustrating a method for processing a hexahedral spherical grating data using a spectroscopic element method digital filter according to the present invention.
FIG. 3 shows a hexahedron (left) and a hexahedron (right) compositional diagram divided into 4x4 elements and a 4x4 grid
Figure 4 shows a hexagonal lattice constellation diagram divided into 8x8 elements
FIG. 5 is a diagram showing a combined discrete Laplacian operator matrix form of elements located at the center (left) and the corner (right) of the face of a hexahedron;
Figure 6 is a graphical representation of the topographic data before and after applying the spectral element method digital filtering for hexahedral spherical grid data
Fig. 7 is a graph showing the seventh day viscoelasticity plotted with a hexahedral spectral element shade model
FIG. 8 shows (a) a local area higher order filter combined with 5x5 elements, (b) a local area higher order filter combined with a 3x3 element, and (c) a RMSE according to the resolution of the light high order filter.

Hereinafter, a preferred embodiment of an apparatus and method for processing hexahedral spherical aberration data using the spectroscopic element method digital filter according to the present invention will be described in detail.

The features and advantages of an apparatus and method for processing hexahedral spherical aberration data using a spectroscopic element digital filter according to the present invention will be apparent from the following detailed description of each embodiment.

FIG. 1 is a block diagram of an apparatus for processing hexahedral spherical aberration data using a spectroscopic element method digital filter according to the present invention, and FIG. 2 is a flowchart illustrating a method for processing a hexahedron spherical aberration data using a spectroscopic element method digital filter according to the present invention. Chart.

The apparatus and method for processing hexahedral spherical grating data using the spectroscopic element method digital filter according to the present invention have improved the efficiency and stability of calculation by constituting a local domain higher order filter using hexahedral spherical spectroscopic element method, and introduces an implicit noise cancellation method to enable stable and accurate filtering.

In addition, the present invention uses a hexahedral spherical spectroscopic element method to ensure high parallel scalability and enables isotropic filtering of high-resolution hexahedral spherical aberration data.

In the following description, the grating data using the hexahedral spherical spectroscopic element method is used as a reference, but it is obvious that it is applicable to the grating data using only the spectroscopic element method.

As shown in FIG. 1, an apparatus for processing hexahedral spherical aberration data using a spectral element method digital filter according to the present invention divides each face of a hexahedron into a finite number of elements by designating the number of elements and lattice points, A hexagonal spherical grating structure 10 having a hexagonal spherical grating structure in which lattice points are defined in an element and a GLLIP constituent element 10 constituting a basis function GLLIP (Gauss-Lobatto-Lagrange Interpolating Polynomial) An operator matrix construction unit 30 for expanding a Laplacian operator using GLLIP and integrating the Laplacian operator for one element to obtain a discrete Laplacian operator matrix for each element, , N _l x N _l and elements combine to local area setting part 40 constituting the Laplacian matrix of the local area, along the engagement element region is defined for each element operator matrix coupling portion 50 for coupling the discrete Laplacian operator matrix A filter matrix construction unit 60 for constructing a discrete filter matrix operator matrix by substituting the discrete Laplacian operator matrix for the local region into the filter equation and a discrete filter matrix operator constructed for each element in advance And an inverse matrix calculation unit 70 for making use of this in calculation.

In the area area setting unit 40, the number of coupling elements N _l is given by FLOOR [6 ^-1 N _e + N ^-1 ], where FLOOR represents the floor function. The coupling region is as shown in Fig.

As shown in FIG. 2, a method for processing a hexahedral spherical lattice data using a spectroscopic element digital filter according to the present invention includes forming a cubic spherical lattice (S201) A step S202 of constructing a local area based on hexahedral lattice setting, and a step S202 of constructing a local area according to a lattice-Lagrange interpolating polynomial (step S202), a Laplacian operator discretization and an operator matrix building step S203 (S205) of constructing a filter matrix for the local region based on the filter equation, a step S206 of calculating a inverse matrix of the filter matrix, and a step S207 of computing the inverse matrix of the filter matrix.

The process of each step of the apparatus and method for processing hexahedral spherical aberration data using the spectroscopic element method digital filter according to the present invention will be described in detail as follows.

A hexahedron can be obtained by projecting a hexahedron on a sphere. The spectral element method is used in which each face of a hexahedron is divided into a finite number of elements and a spectral method is applied in each element.

FIG. 3 is a diagram of a hexahedron (left) and a hexahedron (right) divided into 4 × 4 elements and a 4 × 4 grid. The red line represents the face of the hexahedron, and the blue line represents the element of the hexahedron.

로 정의한다. In Figure 3, the number of elements in a single direction on one side of the hexahedron is

.

The boundaries of the divided elements share the boundaries of neighboring elements and their values.

The Laplacian operator of the hexahedral conformation is given by Equation (1).

과

는 육면체구 격자의 동서 및 남북 지역 좌표를 각각 나타낸다. 육면체구 라플라시안 연산자는 육면체구 분광요소법으로 이산화된다. 육면체구에서 정의되는 적분 가능한 함수를

로 정의하면, 한 요소 내에서 다항 기저함수 전개는 다음과 같다.Where G is the metric tensor of the hexahedron,

and

Represent the coordinates of the east-west and north-south regions of the hexagonal spherical grid, respectively. The hexapole Laplacian operator is discretized by the hexahedral spherical spectroscopic method. The integrable function defined in the hexahedron sphere

, The polynomial basis function expansion within an element is as follows.

Where h is a GLLIP (Gauss-Lobatto-Lagrange Interpolating Polynomial) and N is the order of the basis function.

GLLIP is defined as in Equation (3).

Here, P represents a Reedendre function. We can obtain the discrete Laplacian operator matrix by multiplying the Laplacian operator by the basis function and then integrating it on one element.

Equation (4) can be expressed as a matrix equation using the relationship of the wave-wise function.

는 각각 벡터를 의미한다.Where L is the discrete Laplacian operator matrix, Z and

Respectively denote vectors.

으로 주어진다. 따라서

일 때, 한 요소내의 격자점 수는 16개가 되며 이는 곧 벡터의 길이가 된다.When the order of the basis function is given as N, the total number of lattice points in one element is

. therefore

, The number of grid points in one element is 16, which is the length of the vector.

The matrix of discrete Laplacian operators is a full matrix with a size of 16x16.

The construction of the local domain higher order filter matrix is to construct a higher order filter matrix by combining the discrete Laplacian operators for each element constructed above with a certain number of elements.

For example, considering the accuracy and computational efficiency of a higher order filter, we combine 5x5 elements to construct a higher order filter matrix for the local domain.

An example of the construction of coupling elements on a hexagonal lattice is shown in Fig.

FIG. 4 shows a hexagonal lattice structure divided into 8x8 elements. A blue element indicates a range of elements to be combined, a red element indicates a center thereof, and an element in which actual filtering is performed.

The elements painted in red around the center of (3,3) are combined.

By combining 5x5 elements, the length of the vector is 256, so the size of the combined discrete Laplacian operator is 256x256.

Figure 5 shows the combined discrete Laplacian operator matrix.

Figure 5 shows the combined discrete Laplacian operator matrix form of the elements located at the center (left) and corner (right) of the face of the hexahedron, where non-zero matrix components are denoted by black dots.

The block diagonal shape and the matrix located at the vertex of the hexahedral sphere appear differently due to the characteristics of the position.

This combined discrete Laplacian operator is used to construct a higher order filter.

The higher-order Laplacian filter equation is as shown in equation (5).

Here, g denotes a function to be filtered as a given function, w denotes a filtered function, v denotes a filter coefficient, and q (positive integer) denotes a filter order.

)을 바탕으로, 고차 필터방정식을 행렬방정식으로 표현하면 수학식 6에서와 같다.The discrete Laplacian operator matrix (

), The higher order filter equation can be expressed by the matrix equation as shown in Equation (6).

은 고차 필터행렬을 의미한다. 따라서 지역 영역의 이산 라플라시안 연산자를 구축하였다면, 고차 필터행렬은 간단히 구축할 수 있다.here,

Means a higher order filter matrix. Therefore, if we construct a discrete Laplacian operator in the local domain, the higher order filter matrix can be constructed simply.

The process of filtering is performed by matrix-vector multiplication with a given function by inversely multiplying the higher-order filter matrix.

The inverse matrix of the higher order filter matrix is calculated in advance and can be repeatedly used at every filtering.

After the filtering is performed, the elements of (3, 3) located at the center of FIG. 4 are left, and the elements of (3, 3) left after the calculation for each coupling element share the boundary value.

와

에 따른 가장 작은 규모의 성분이 그 절반이 되도록 설정한다.That is, it has a boundary and a mean value of neighboring elements. The rate of amplitude reduction due to filtering is determined by a given resolution,

Wow

Is set to be half thereof.

)와 진폭감소비율(

)을 정하면, 다음의 수학식 8에 의해 결정된다.The order of the filter (

) And amplitude reduction ratio (

) Is determined by the following equation (8).

,

이며,

은 주어진

와 에 따른 지구 반지름으로 무차원화 된 최저 격자 간격이다.here,

,

Lt;

Given

Wow Is the minimum lattice spacing that is non-dimensional to the Earth's radius according to

The apparatus and method for processing hexahedral spherical aberration data using the spectral element method digital filter according to the present invention having the above-described structure are applied to the interpolated topographic data as the hexahedral spherical aberration, and the filtering performance is confirmed as follows.

The topographic data used were terrain data provided by the National Oceanic and Atmospheric Administration (NOAA) of the US Maritime Authority, and were originally provided on the latitude and longitude coordinates, but were interpolated into hexagonal sphere.

,

,

,

로 설정하였다.After interpolation, topographic data were smoothed by applying an apparatus and method for processing hexahedral spherical grating data using a spectroscopic element method digital filter according to the present invention,

,

,

,

Respectively.

For the visual ease after smoothing, the results were compared by interpolating the hexagonal lattice to the lattice lattice.

Figure 6 compares the results before and after smoothing of topographic data.

After the smoothing, the shape of the coastline has become gentle, and the small islands have been removed.

This means that the apparatus and method for processing hexahedral spherical aberration data using the spectroscopic element method digital filter according to the present invention are applied to precisely perform smoothing of hexahedron spherical aberration data.

The use of the hexahedral spectral element model as a filter for the removal of the numerical noise is described as follows.

An apparatus and method for processing hexahedral spherical grating data using the spectroscopic element method digital filter according to the present invention is applied as a filter for removing the numerical noise of the hexahedron spectral element shade model.

We selected the standard model 5, which simulates the wind field on the terrain, and replaced the terrain with the actual observational terrain to generate more numerical noise.

와

으로, 고차 필터는

,

로 설정하였다.This product was applied every step of time to remove the numerical noise of the model. Horizontal resolution corresponds to about 1 degree of light bulb

Wow

, The higher order filter

,

Respectively.

Experiments were carried out for 7 days to compare the results with the previously used explicit viscous treatment method and the implicit viscous treatment method (bulb high - order filter) which connects all the elements constituting the hexahedron.

FIG. 7 is a diagram of the seventh day visibility field simulated by a hexahedral spectral element water flow model. FIG.

이며, 등치선 간격은

이다.(a) is a local area high-order filter to which the present invention is applied, (b) is a high-order high-order filter, (c) is a 7-day long field simulated by a hexahedral spectral element The

And the isochronous interval is

to be.

In the prior art, the explicit viscous processing method, which is widely used in the hexahedral spectral element model, can not properly remove the numerical noise, so that the numerical noise is generated in some areas and the visibility is distorted.

On the other hand, it can be seen that the numerical noise is removed in the result of the local area high-order filter and the high-order light filter having the present invention.

It can be seen that the local area higher order filter to which the present invention is applied is very similar to the light source higher order filter to be compared because the two filters are implemented in the same manner.

However, due to the difference in the number of elements to be combined, there is a considerable difference in calculation time.

The local domain higher order filter has advantages over the computation time because the number of elements to be combined is smaller than that of the global high order filter.

Table 1 compares the filter matrix inversion time and the filter execution time of the local domain high-order filter and the high-order filter with the resolution, respectively.

Table 1 shows the inverse time of the filter matrix and the filter execution time according to the horizontal resolution. The filter execution time is a time when 100 filters are applied.

LIMP is a local area high order filter, and GIMP is a global high order filter.

일 때 지역 영역 고차 필터에서 약 74배 정도 계산 시간이 감소하였다. 또한 필터 수행 시간의 경우, 약 2.4배 정도 계산 시간이 감소하는 것을 확인할 수 있다.If the inverse time of the filter matrix,

The computation time was reduced about 74 times in the local domain high - order filter. Also, it can be confirmed that the calculation time is reduced by about 2.4 times in the case of the filter execution time.

And FIG. 8 is an RMSE according to the resolution of (a) a local area higher-order filter combined with 5x5 elements, (b) a local area higher-order filter combined with 3x3 elements, and (c)

The local area higher order filter according to the present invention has a higher calculation efficiency than that of the light source high order filter and its accuracy is also made to correspond to the light source higher order filter by combining 5x5 elements.

The error convergence rate was calculated using the Rossby-Haurwitz wave as an analytic solution. It can be seen that not only the absolute size of the error but also the convergence rate of the error are very similar in the high-order filter and the high-order filter of the region. However, when the 3 × 3 elements are combined, the error magnitude is not only large but also the error convergence rate is very low, about two orders of magnitude.

The apparatus and method for processing hexahedral spherical grating data using the spectroscopic element method digital filter according to the present invention not only show a more stable viscous processing performance as compared with the previously used explicit viscous processing method, It means that the accuracy is maintained and can be processed at higher speed.

As described above, it will be understood that the present invention is implemented in a modified form without departing from the essential characteristics of the present invention.

It is therefore to be understood that the specified embodiments are to be considered in an illustrative rather than a restrictive sense and that the scope of the invention is indicated by the appended claims rather than by the foregoing description and that all such differences falling within the scope of equivalents are intended to be embraced therein It should be interpreted.

10. Hexagonal spherical grid component 20. GLLIP component
30. Operator matrix construction unit 40. Local area setting unit
50. Operator matrix combining unit 60. Filter matrix building unit
70. Inverse matrix calculation unit

Claims (15)

A hexahedral sphere lattice component with a hexagonal sphere lattice structure;
For discretization using the spectral element method, a GLLIP constituent part constituting a basis function GLLIP (Gauss-Lobatto-Lagrange Interpolating Polynomial);
An operator matrix building unit for developing a Laplacian operator using GLLIP and integrating the Laplacian operator for one element to obtain a discrete Laplacian operator matrix for each element;
N _l x A local region setting unit which combines N _l elements to construct a Laplacian matrix for the local region;
An operator matrix combining unit for combining discrete Laplacian operator matrices along a joint element area defined for each element;
And a filter matrix building unit for constructing a discrete filter matrix operator matrix by substituting the discrete Laplacian operator matrix for the local region into the filter equation and performing a hexagonal sphere lattice data processing using the spectral element method digital filter. . The apparatus of claim 1, wherein the hexahedral sphere lattice-
Wherein a user designates the number of elements and lattice points and divides each face of the hexahedral element into a finite number of elements and a lattice point is defined in each element. Apparatus for processing old grid data. The apparatus as claimed in claim 1, further comprising an inverse matrix calculator for inversely calculating a discrete filter matrix operator constructed for each element and using the inverse matrix matrix operator for calculation. Device. The apparatus according to claim 1,
Wherein the number of coupling elements N _l is given by FLOOR [6 ^-1 N _e + N ^-1 ], where FLOOR is the bottom function. Forming a hexagonal spherical grid;
A GLLIP constructing step to construct a basis function GLLIP (Gauss-Lobatto-Lagrange Interpolating Polynomial) for discretization using the spectroscopic element method;
An operator matrix building step of developing a Laplacian operator using GLLIP and integrating the Laplacian operator for one element to obtain a discrete Laplacian operator matrix for each element;
N _l x A local region setting step of combining N _l elements to construct a Laplacian matrix for the local region;
An operator matrix combining step of combining a discrete Laplacian operator matrix along a joint element area defined for each element;
And a filter matrix constructing step of constructing a discrete filter matrix operator matrix by substituting the discrete Laplacian operator matrix for the local region into the filter equation and constructing a discrete filter matrix operator matrix using the discrete Laplacian operator matrix. Way. 6. The method of claim 5, further comprising a inverse matrix calculation step of inverting the discrete filter matrix operator constructed for each element in advance and utilizing it in a calculation. Way. 6. The method of claim 5, wherein in the step of configuring the hexagonal sphere lattice,
The number of elements in a single direction on one side of the hexahedron

, The boundaries of the divided elements share the boundaries of neighboring elements, and the Laplacian operator of the hexahedron design is defined as:

Lt; / RTI >
Where G is the metric tensor of the hexahedron,

and

Wherein the coordinates represent the coordinates of the east-west and north-south regions of the hexagonal spherical grating, respectively. 8. The method of claim 7 wherein the cubic laplacian operator is discretized by a hexahedral spectral element method,
The integrable function defined in the hexahedron sphere

, The polynomial basis function expansion within an element can be expressed as:

ego,
Wherein h is a GLLIP (Gauss-Lobatto-Lagrange Interpolating Polynomial) and N is a degree of a basis function. A method for processing a hexahedron sphere data using a spectral element method digital filter. 6. The method of claim 5, wherein in the GLLIP configuration step,
GLLIP

Lt; / RTI >
Wherein P represents a Reedendre function. The method for processing a hexahedral sphere lattice data using a spectral element method digital filter. 6. The method of claim 5, wherein in the step of constructing the operator matrix,
When the matrix function is multiplied by the basis function and then the integral of the Laplacian operator is integrated to obtain a discrete Laplacian matrix,

ego,
Where L is the discrete Laplacian operator matrix, Z and

Wherein each of the vectors represents a vector. A method for processing a hexahedral spherical aberration data using a spectral element method digital filter. 6. The method of claim 5, wherein in a filter matrix building step of substituting the filter equation into a filter equation and constructing a discrete filter matrix operator matrix,
The filter equation,

Lt; / RTI >
Where g is a function to be filtered as a given function, w is a filtered function, v is a filter coefficient, and q (positive integer) is the order of the filter. A method for the processing of hexahedral sphere data using elemental digital filters. 12. The method of claim 11, wherein the discrete Laplacian operator matrix (

), The filter equation is expressed by a matrix equation,

ego,
here,

Is a high order filter matrix. A method for processing hexahedral spherical aberration data using a spectral element method digital filter. 13. The method of claim 12, wherein the performing of the filtering is performed by matrix-vector multiplication of a higher order filter matrix and a given function,

A method for processing hexahedral spherical aberration data using a spectral element method digital filter. 14. The method of claim 13, wherein the inverse matrix of the higher order filter matrix is calculated and used repeatedly each time filtering is performed,
After the filtering is performed, only the elements located at the center of the hexagonal lattice are left, and when the calculation is completed for each coupling element, the remaining elements share the boundary value and have the average value and the boundary of the neighboring elements. A method for processing hexahedral sphere data. 14. The method of claim 13, wherein the amplitude reduction ratio by filtering is a given resolution

Wow

The smallest scale component is set to be half thereof,
The order of the filter (

) And amplitude reduction ratio (

),

Lt; / RTI >
here,

,

Lt;

Given

Wow

Wherein the minimum lattice spacing is a dimensionless non-dimensional lattice spacing.

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