TWI597686B - A method and apparatus for executing high performance computation to solve pdes and for outputting three-dimensional interactive images in collaboration with a gpu is disclosed - Google Patents

Description

Collaborative GPU as a method, device and computer readable recording medium and computer program product for solving high-performance operation and three-dimensional interactive image output of partial differential equation

The invention relates to a cooperative GPU as a method and device for solving high-performance computing and three-dimensional interactive image output of Partial Differential Equations (PDEs), and a computer readable recording medium and a computer program product, in particular, The GPU performs PDEs calculations, and based on the operation results, the 3D interactive images and output persons with physical changes are completely drawn by the GPU.

Due to the rapid development of science and technology, high-performance computing has been widely used in research related to people's livelihood, such as medical diagnosis, 3D interactive teaching, global climate change, typhoon, tsunami, earthquake and other natural disaster energy transfer and damage prediction. Therefore, the importance of large-scale computational simulations has gradually received attention. With its low cost and low power consumption, GPU has become an alternative to CPU as a high-performance alternative.

Augmented reality for the establishment of simulated boundary conditions (Augmented Reality, AR) imagery is a novel and fast method of image input that can be used to create many models for simulation, such as buildings, human organs or natural environments.

However, the current GPU is used as a method for solving the high-performance operation of partial differential equations. Traditionally, only part of the work is performed by the GPU device. For example, in the fifth figure, in the cooperative operation of the CPU and the GPU in the figure: the dotted square represents the CPU. The instructions required by the GPU, the solid line squares represent the position where the calculation workload is executed, the single solid arrow represents the data transfer between the CPU and the GPU, and the double solid arrow represents the progress of the entire operation simulation by the CPU management. It can be seen that both CPU and GPU involve data transmission during the operation process. In the process of mass data transmission, the image delay output is often caused, and the GPU still has more than half of the time in the whole operation process, and the GPU performance cannot be fully utilized.

In addition, if only the CPU-driven Augmented Reality technology is used, and the simulation results obtained by the high-performance calculation are presented, the problem that the 3D motion image cannot be output immediately (REAL TIME) is encountered.

Referring again to the sixth figure, for the separation flux (F=f(Q)) step of the GPU operation finite volume method in the fifth figure, for a single-core GPU, it is necessary to find an adjacent computing unit at a cost. When the required calculation data is large, it is sometimes one of the factors that cause image delay output.

In order to fully exploit the advantages of GPU high-performance computing and overcome the problem of image output delay, the present invention predicts that the simulation operation of PDEs is completely executed by the GPU, and the simulation result is completely executed by the GPU to perform drawing and output to achieve instant ( REAL TIME) Outputs the effect of missing image delays.

The invention further proposes a technology for utilizing Augmented Reality (AR) as a three-dimensional image input, the CPU performs the establishment of the augmented reality three-dimensional image, and sets the coordinates and boundary conditions according to the three-dimensional image, and combines the high performance of the GPU. The operation can integrate the augmented reality 3D images to instantly output 3D interactive images with physical quantity changes.

Therefore, the present invention is a cooperative GPU as a method for solving high-performance operations and three-dimensional interactive image output of partial differential equations (PDEs), including the following steps: A. Performing coordinate conversion of a three-dimensional image by the CPU, and converting the result according to coordinates Set the boundary conditions required for the simulation, and input the boundary conditions to the GPU, that is, calculate the coordinate values of the 3D image as the boundary conditions of the PDEs simulation; B. The GPU performs a partial differential equation according to the boundary conditions provided in Step A. Numerical simulation; C. GPU calculates drawing elements according to numerical simulation results, and draws visual images with physical quantity changes on the three-dimensional images to form a three-dimensional interactive image to be output by a display unit.

Further, in steps B and C, the data transfer between the CPU and the GPU only involves the CPU transmitting the work instruction to the GPU, and after the GPU completes the work, transmitting the feedback instruction to the CPU.

Further, the numerical simulation of step B uses a finite volume method, including calculating the separation flux of the finite volume method and calculating the state of the finite volume method.

Further, in step C, the GPU accelerates the rendering speed in conjunction with the CUDA syntax.

Further, the three-dimensional image of step A is an augmented reality image generated by a photographing unit that captures a marked photographed image, and the mark may be a physical object or a projected image.

Further, before performing step A, the CPU first performs computer system program initialization setting work, including the following steps: A1. The display unit is displayed in the display unit to be initialized; A2. CPU specifies the memory space required by the computer host. ; A3. Copy the partial differential equation of the desired simulation to the memory space of the GPU; A4. Start the camera unit using the Augmented Reality tool.

Further, after step C, step D is included, and the CPU executes the computer system program to end the work, including the following steps: D1. releasing the memory space of the GPU; D2. releasing the memory space of the computer host; D3. ending the photographing unit. Operation; D4. End the operation of the display unit.

The present invention is also a device for cooperating with a GPU as a high-performance computing and three-dimensional interactive image output for solving partial differential equations. The device includes: a computer host including a CPU, a GPU and an application installed thereon; a computer host; a display unit electrically connected to the computer host; the application is configured to enable the computer host to execute a collaborative GPU as a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, and displaying the method on the display unit A three-dimensional interactive image of the results of the operation.

Further, the device is any one of a personal computer, a game console or a smart handheld device.

The invention also relates to a computer readable recording medium, which is an application program, which enables a computer host to execute a collaborative GPU as a solution to a partial differential equation. High-performance computing and 3D interactive image output methods.

The invention is also a computer program product for installing an application on a computer host, the application enabling the computer host to execute a collaborative GPU as a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output.

The invention has the following effects:

1. The GPU is used to process complex operations related to physical quantities, and the operation result can be outputted in an efficient manner, and the output result includes at least an instantaneous physical quantity change and a smooth dynamic three-dimensional interactive image.

2. Utilizing the powerful computing functions of the GPU, the simulation cost of executing real-time 3D interactive images can be greatly reduced.

3. Augmented reality is no longer just a three-dimensional dynamic image, but includes the interaction between objects under specific parameters, and thus includes three-dimensional real-time simulation results of complex physical quantities.

4. During the simulation, any parameter or object transformation can get fast and immediate calculation results and output immediately.

5. Make complex calculations with high-speed output, instant and dynamic 3D interactive images up to 200 fps output, and more.

6. The result of high efficiency output is more convenient to observe the subtle changes of any object during the simulation.

The first figure is a schematic flow chart of the CPU and GPU cooperative operation of the present invention.

The second figure is a schematic diagram of calculating the separation flux using a single calculation unit in the step C of the embodiment of the present invention.

The third figure is a schematic diagram of the GPU combined with the CUDA syntax acceleration operation in the step D of the embodiment of the present invention.

The fourth figure is a simplified flow diagram of the CPU and GPU cooperative operation, illustrating that the method of the present invention has a higher performance operation (HPC) than the conventional method.

The fifth figure is a schematic flow chart of the conventional CPU and GPU cooperative operation.

The sixth figure is a schematic diagram of a conventional GPU computing separation flux.

Based on the above technical features, the main functions of the GPU as a method and device for solving the high-performance operation and the three-dimensional interactive image output of the partial differential equation and the computer readable recording medium and the computer program product can be clearly demonstrated in the following embodiments.

Referring to the first figure, in the embodiment of the present invention, the CPU is used to process the augmented reality image, and the simulation conditions are given, and then the complex PDEs operation is completely executed by the GPU, and the high-performance operation of the GPU can be quickly performed. Calculate the result of the physical quantity change represented by the PDEs, and plot the result of the physical quantity change into a visual image overlay on the augmented reality 3D image, so that the augmented reality image can be output immediately (REAL TIME) 3D interactive image with physical quantity change; in the diagram of the CPU and GPU collaborative operation: the dotted square represents the instruction that the CPU requires the GPU to execute, the solid line represents the position where the calculation workload is executed, and the single solid arrow represents the CPU and GPU. Data transfer, single-dotted arrow represents the transfer of work instructions and feedback instructions between the CPU and GPU, double solid line represents the CPU management to master the entire operation simulation, and finally the thick solid line represents the GPU drawing output by the display unit.

The steps of this embodiment include:

A. The computer system program initialization setting work is performed by the CPU. The system program initialization setting work includes the following steps:

A1. The drawing application is initialized in a display unit, such as an application such as OpenGL, DirectDraw or DirectX.

A2. CPU specifies the memory space required by the host computer.

A3. Copy the required partial differential equations (PDEs) to the memory space of the GPU.

A4. Start a camera unit using the Augmented Reality tool.

B. Using augmented reality (AR) technology, a photographing image of a marker is taken by the photographing unit, and an augmented reality three-dimensional image is generated by recognizing the photographed image, wherein the mark may be an entity The object mark or the projection image mark generated by the projector, and then the coordinate conversion of the augmented reality 3D image is performed by the CPU, and the boundary condition required for the simulation is set according to the coordinate conversion result, that is, the coordinates of the 3D image are calculated. Value, as a boundary condition for PDEs simulation, and input boundary conditions to the GPU.

C. GPU performs the numerical operation of PDEs according to the partial differential equation provided in step A and the boundary conditions provided in step B, taking the finite volume method as an example, involving the calculation of the separation flux of the finite volume method and the calculation of the state of the finite volume method. As shown in the first figure, the CPU will issue a work command of “calculate the split flux of the finite volume method” to the GPU, and the GPU will perform the operation. After the GPU operation is completed, a feedback command will be transmitted to the CPU, and the CPU receives the operation. After the feedback command, release the next work order "Calculation The state of the finite volume method to the GPU, the GPU performs the operation, and repeats the aforementioned operation mode, and after the GPU is finished, transmits a feedback instruction to the CPU.

Referring to the second figure, the present invention can effectively calculate the separation flux (F=f(Q)) using a single computing unit for a single-core GPU, without wasting computational cost to find adjacent computing units, and computing efficiency. good.

D. Referring to the first figure, after the CPU receives the feedback command to confirm that the GPU completes the PDEs operation, the CPU will ask the GPU to perform the drawing work, including calculating the drawing elements and drawing the image output to the display unit, wherein the CPU first releases The work instruction of the "calculation drawing element" is sent to the GPU, and the GPU calculates the drawing element according to the numerical simulation result. After the GPU operation is completed, a feedback instruction is transmitted to the CPU, and after receiving the feedback instruction, the CPU issues the next work instruction "drawing output". To the GPU, the GPU can draw a visual image with a change in physical quantity superimposed on the aforementioned three-dimensional image, and form a three-dimensional interactive image to be output by the display unit.

Among them, please refer to the third figure. In the operation of step D, the GPU is combined with the CUDA syntax to speed up the rendering, mainly using the CUDA syntax core to process the data (P) from the structure memory space, and execute the time. The desired index conversion (I _R =T(X)). The CUDA syntax core then redefines the color (C) and vertex (V) and stores the data in the overall memory space before Rendering.

In step C and step D, the data transfer between the CPU and the GPU only involves the CPU transmitting the work instruction to the GPU, and after the GPU finishes working, transmitting the feedback instruction to the CPU, completely processing the complex operation related to the physical quantity by the GPU, and The GPU completely executes the drawing output, so through the high-performance computing of the GPU itself, the instant output contains dynamic 3D interactive images with physical changes and smooth images; For simulation work, step B to step D can be repeated to output different simulation results in real time.

E. After the simulation work is completed, the CPU finally executes the computer system program to end the work, including the following steps:

E1. Free up the GPU's memory space.

E2. Release the memory space of the host computer.

E3. End the operation of the photographing unit.

E4. End the operation of the display unit.

End the computer system work through the above procedure.

The following is a scientific calculation theory. In the CPU and GPU cooperative operation of the present invention, the PDEs are completely executed by the GPU and the graphics output is completely executed by the GPU to obtain the result of High Performance Computing (HPC): As shown in the figure, the acceleration effect of the calculation of the present invention is verified by Gustafson's Law: SU = a + P (1- a )

Among them, the SU table speed-up, the fraction of work that cannot be parallelized, the number of processors. Let the initialization process consume resources: F _INIT = k _INIT N

Where N is the number of cells, and K _INIT consumes resources for each cell initialization process.

Assume that the resources required to perform Work A and Work B in the diagram are linear with N: F _A = k _A N F _B = k _B N

Where k _A and k _B are resources that are consumed during the calculation of each computing unit.

The communication between the CPU and the GPU requires resources: F _COM = k _COM N

Among them, K _COM requires resources for communication between the CPU and the GPU for each computing unit.

It is obtained by Gustafson’s Law:

(I) When Work A and Work B are operated in parallel by the CPU and GPU, that is, the PDEs and partial plot outputs of the CPU and GPU are processed separately: and

(II) When Work A and Work B are completely parallelized by the GPU, that is, when the PDEs operation and drawing output are completely processed by the GPU: and

We also define:

Among them, SU _R represents the acceleration ratio when the parallel operation is completely performed by the GPU and the parallel operation is performed by the CPU and the GPU at the same time. available:

After simplification, you get:

Through the foregoing calculation formula, it can be found that the SU _{R is} greater than 1, that is, the present invention does achieve a higher performance operation (HPC) than the conventional CPU and GPU cooperative operation.

Since the present invention utilizes the high-performance computing (HPC) feature of the GPU, the GPU is used to perform PDEs calculations and the GPU is completely executed by the GPU. Therefore, for 3D image simulation involving kinetic energy transfer, such as tsunami, earthquake, typhoon and the like, 3D image simulation of damage effects; or 3D image simulation involving vibration, such as metal fatigue simulation under vibration or simulation of seismic strength of buildings; or 3D image simulation involving fluid mechanics, such as traffic vehicles (aircraft, automobiles) Simulation of air resistance; or simulations involving impact damage, such as vehicle crash experiments and designs, can be simulated immediately (REAL TIME).

In view of the above description of the embodiments, the operation, the use and the effects of the present invention can be fully understood, but the above embodiments are merely preferred. The scope of the invention is to be construed as being limited by the scope of the invention and the scope of the invention.

Claims (33)

A cooperative GPU is used as a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, and the steps include: A. performing coordinate conversion of a three-dimensional image by the CPU, and setting boundary conditions required for the simulation according to the coordinate conversion result, and The boundary condition is input to the GPU, that is, the coordinate value of the PDEs is calculated by calculating the coordinate value of the 3D image; B. GPU performs a numerical simulation of the partial differential equation according to the boundary condition provided by the step A; C. GPU is based on the numerical simulation result The drawing element is calculated, and the visual image with the physical quantity change is drawn on the aforementioned three-dimensional image, and the three-dimensional interactive image is formed and output by a display unit. For example, in the method of claim 1, the cooperative GPU is used as a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output. In steps B and C, the data transmission between the CPU and the GPU involves only the CPU transmission work. The instruction is sent to the GPU, and after the GPU finishes working, the feedback instruction is transmitted to the CPU. For example, the cooperative GPU described in claim 1 is a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, wherein the numerical simulation of the step B uses a finite volume method, including the calculation of the separation flux of the finite volume method. And calculate the state of the finite volume method. For example, the collaborative GPU described in claim 1 is a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output. In step C, the GPU Combine CUDA syntax to speed up calculations. For example, the cooperative GPU described in claim 1 is a high-performance operation for solving partial differential equations and a method for outputting three-dimensional interactive images, wherein the three-dimensional image of step A is generated by a photographing unit to capture a marked image. Increase the reality image. The cooperative GPU as described in claim 5 of the patent application is a method for solving high-performance operations and three-dimensional interactive image output of a partial differential equation, wherein the mark is a solid object or a projected image. For example, the collaborative GPU described in claim 5 is a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output. Before performing step A, the CPU first executes the computer system program initialization setting work, including the following Step: A1. In the foregoing display unit, the drawing application is initialized; A2.CPU specifies the memory space required by the host computer; A3. Copy the required differential partial equation to the GPU memory space; A4. The augmentation tool launches the camera unit. For example, the cooperative GPU described in claim 5 is a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output. After the step C, the step D is included: the computer system program is executed by the CPU, including the following Step: D1. Release the memory space of the GPU; D2. Release the memory space of the computer host; D3. End the operation of the photographing unit; D4. End the operation of the display unit. A cooperative GPU as a high-performance operation and three-dimensional mutual solution for solving partial differential equations The image output device includes: a computer host including a CPU, a GPU and an application installed on the computer host; a display unit electrically connected to the computer host; the application is used for The computer host executes the cooperative GPU as a method for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, and the method steps include: A. performing coordinate conversion of a three-dimensional image by the CPU, and setting a simulation required according to the coordinate conversion result The boundary condition, and the boundary condition is input to the GPU, that is, the coordinate value of the PDEs is calculated by calculating the coordinate value of the three-dimensional image; B. GPU performs a numerical simulation of the partial differential equation according to the boundary condition provided by step A; The GPU calculates a drawing element according to the numerical simulation result, and draws a visual image with a physical quantity change superimposed on the aforementioned three-dimensional image to form a three-dimensional interactive image to be output by the display unit. For example, the collaborative GPU described in claim 9 is a device for solving the high-performance operation and the three-dimensional interactive image output of the partial differential equation, wherein the computer host performs the data transmission between the CPU and the GPU in steps B and C. It involves the CPU transmitting the work instruction to the GPU, and after the GPU finishes working, transmitting the feedback instruction to the CPU. For example, the collaborative GPU described in claim 9 is a device for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, wherein the computer host performs the numerical simulation of step B using the finite volume method, including the calculation of the finite volume method. The separation flux and the state of the finite volume method are calculated. For example, the collaborative GPU described in claim 9 is a device for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, wherein the computer host performs step C, and the GPU combines the CUDA syntax to accelerate the calculation speed. The device as claimed in claim 9 is the device for solving the high-performance operation and the three-dimensional interactive image output of the partial differential equation, and further comprising a camera unit electrically connected to the computer host, wherein the computer host performs the three-dimensional image of step A. The augmented reality image produced by the photographing image of the mark is taken by the photographing unit. For example, the collaborative GPU described in claim 13 is a device for solving high-performance operations and three-dimensional interactive image output of a partial differential equation, wherein the mark is a physical object or a projected image. For example, the collaborative GPU described in claim 13 is a device for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, wherein the computer host performs the initialization of the computer system program by the CPU before executing step A. , including the following steps: A1. In the foregoing display unit display drawing application is initialized; A2. CPU specifies the memory space required by the host computer; A3. Copy the required differential partial equation to the GPU memory space; A4. Launch the camera unit using the Augmented Reality tool. For example, the collaborative GPU described in claim 13 is a device for solving the high-performance operation and the three-dimensional interactive image output of the partial differential equation, wherein the computer host executes step C and then executes step D: executing the computer system program by the CPU. End the work, including the following steps: D1. Release the memory space of the GPU; D2. Release the memory space of the computer host; D3. Ending the operation of the photographing unit; D4. Ending the operation of the display unit. For example, the cooperative GPU described in claim 9 is a device for solving the high-performance operation of the partial differential equation and the three-dimensional interactive image output, and the device is any one of a personal computer, a game console or a smart handheld device. A computer readable recording medium is an application that causes a computer host to execute a collaborative GPU as a method for solving high-performance operations of a differential equation and a three-dimensional interactive image output. The steps of the method include: The CPU performs a coordinate conversion of a three-dimensional image, and sets a boundary condition required for the simulation according to the coordinate conversion result, and inputs the boundary condition to the GPU, that is, calculates a coordinate value of the three-dimensional image as a boundary condition of the PDE simulation; The GPU performs a numerical simulation of a partial differential equation according to the boundary condition provided by step A; C. GPU calculates a drawing element according to the numerical simulation result, and draws a visual image with a physical quantity change superimposed on the three-dimensional image to form a three-dimensional interactive image. Display unit output. For example, in the computer-readable recording medium described in claim 18, in step B and step C, the data transmission between the CPU and the GPU only involves the CPU transmitting the work instruction to the GPU, and after the GPU completes the work, transmitting the feedback. Command to the CPU. The computer-readable recording medium according to claim 18, wherein the numerical simulation of step B uses a finite volume method, including calculating a separation flux of the finite volume method and calculating a state of the finite volume method. As in the computer-readable recording medium described in claim 18, in step C, the GPU accelerates the calculation speed in conjunction with the CUDA syntax. The computer-readable recording medium according to claim 18, wherein the three-dimensional image of step A is an augmented reality image generated by a photographing unit that captures a marked photographed image. The computer-readable recording medium of claim 22, wherein the mark is a physical object or a projected image. For example, in the computer-readable recording medium described in claim 22, before performing step A, the CPU first executes the computer system program initialization setting work, including the following steps: A1. Displaying the drawing application in the foregoing display unit Initialized; A2.CPU specifies the memory space required by the host computer; A3. Copy the partial differential equation of the desired simulation to the memory space of the GPU; A4. Start the camera unit using the Augmented Reality tool. For example, the computer readable recording medium described in claim 22, after step C, includes step D: the computer system program execution is completed by the CPU, including the following steps: D1. releasing the GPU memory space; D2 .Release the memory space of the host computer; D3. End the operation of the photographing unit; D4. End the operation of the display unit. A computer program product for installing an application on a computer host, the application causing the computer host to execute a collaborative GPU as a method for solving high-performance operations and three-dimensional interactive image output of a partial differential equation, the method comprising the steps of: Performing coordinate conversion of a 3D image by the CPU, setting the boundary conditions required for the simulation according to the coordinate conversion result, and inputting the boundary condition to the GPU, That is, by calculating the coordinate value of the 3D image as the boundary condition of the PDE simulation; B. GPU performs a numerical simulation of the partial differential equation according to the boundary condition provided by the step A; C. GPU calculates the drawing element according to the numerical simulation result, and draws with A visual image of a change in physical quantity is superimposed on the aforementioned three-dimensional image, and a three-dimensional interactive image is formed by a display unit. For example, in the computer program product described in claim 26, in step B and step C, the data transfer between the CPU and the GPU only involves the CPU transmitting the work instruction to the GPU, and after the GPU completes the work, transmitting the feedback instruction to the CPU. . The computer program product of claim 26, wherein the numerical simulation of step B uses a finite volume method, including calculating the separation flux of the finite volume method and calculating the state of the finite volume method. In the computer program product described in claim 26, in step C, the GPU combines the CUDA syntax to speed up the calculation. The computer program product of claim 26, wherein the three-dimensional image of step A is an augmented reality image generated by a photographing unit that captures a marked image. The computer program product of claim 30, wherein the mark is a physical object or a projected image. For example, in the computer program product described in claim 30, before performing step A, the CPU first executes the computer system program initialization setting work, including the following steps: A1. The display unit is displayed in the display unit to be initialized; A2. CPU specifies the memory space required by the host computer; A3. Copy the partial differential equation of the desired simulation to the memory space of the GPU; A4. Start the camera unit using the Augmented Reality tool. For example, the computer program product described in claim 30, after step C, includes step D: the computer system program is executed by the CPU, including the following steps: D1. releasing the memory space of the GPU; D2. releasing the computer The memory space of the host; D3. Ending the operation of the photographing unit; D4. Ending the operation of the display unit.